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Page No 99:

Question 1:

Add the following expressions:

(i) 5x, 7x, −6x
(ii) 35x,23x,-45x
(iii) 5a2b, −8a2b, 7a2b
(iv) 34x2,5x2,-3x2,-14x2
(v) x − 3y + 4z, y − 2x − 8z, 5x − 2y − 3z
(vi) 2x2 − 3y2, 5x2 + 6y2, − 3x2 − 4y2
(vii) 5x − 2x2 − 8, 8x2 − 7x − 9, 3 + 7x2 − 2x
(viii) 23a-45b+35c,-34a-52b+23c,52a+74b-56c
(ix) 85x+117y+94xy,-32x-53y-95xy
(x) 32x3-14x2+53,-54x3+35x2-x+15,-x2+38x-815

Answer:

(i)
  5x + 7x + (-6x)
= 5x + 7x -6x
= 6x

(ii)

 35x +23x +-45x=9x +10x -12x15=7x15

(iii) 
5a2b +( −8a2b)  + 7a2b
= 5a2b − 8a2b + 7a2b
4a2b

(iv)
  34x2 + 5x2+ (-3x2 ) + (-14x2)=34x2 - 14x2 + 5x2-3x2=12x2 + 2x2 = 52x2


(v)
Collecting like terms and adding them:

x − 3y + 4z + y − 2x − 8z + 5x − 2y − 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z        
= 4x -4y -7z

(vi) Collecting like terms and adding them:
2x2 − 3y2 + 5x2 + 6y2 + (− 3x2 − 4y2)
 = 2x2 + 5x2 - 3x2 - 3y2 +6y2 -4y2= 4x2 -y2                   

(vii) Collecting like terms and adding them:
5x − 2x2 − 8 +  8x2 − 7x − 9 +  3 + 7x2 − 2x
= -2x2 +8x2 + 7x2 + 5x - 7x - 2x -8 -9 + 3= 13x2 -4x -14      


(viii) Collecting like terms and adding them:

23a-45b+35c +-34a -52b+23c + 52a+74b- 56c   b -52b +74b +35c +23c - 56c =(8 -9 +30)a12 + (-16 - 50 +35)b20 + (18 +20 -25)c30=2912a - 3120b + 1330c


(ix) Collecting like terms and adding them:
85x+ 117y+94xy + - 32x- 53y-95xy=85x - 32x+ 117y - 53y +94xy -95xy = 110x - 221y + 920xy

(x) Collecting like terms and adding them:
32x3-14x2 +53+- 54x3+35x2- x+15+- x2  +38x-815= 32x3 - 54x3 -14x2 +35x2- x2  - x +38x +53+15-815=14x3 - 1320x2 -58x +43x+117y+94xy,32x53y9

Page No 99:

Question 2:

Subtract:

(i) −8xy from 7xy
(ii) x2 from − 3x2
(iii) (x − y) from (4y − 5x)
(iv) (a2 + b2 2ab) from (a2 + b2 + 2ab)
(v) (x2 − y2) from (2x2 − 3y2 + 6xy)
(vi) (x − y + 3z) from (2zx − 3y)

Answer:

(i) 7xy- (-8xy)
= 7xy+ 8xy
= 15xy

(ii)  - 3x2 - x2
= -4x2

(iii)  (4y - 5x) - (x- y)
= 4y - 5x - x + y
= 5y - 6x

(iv)
(a2 + b2 + 2ab) - (a2 + b2 2ab)
= a2 -a2 +b2 -b2 + 2ab + 2ab    (Collecting like terms and adding them)
= 4ab

(v)
(2x2 − 3y2 + 6xy) -  (x2y2)
2x2 - x2 - 3y2 + y2 +6xy=x2 -2y2 +6xy     (Collecting like terms and adding them)

(vi)  (2z -x -3y) - (x - y +3z)
= 2z -3z -x -x -3y +y       (Collecting like terms and adding them)
= -z -2x - 2y 

Page No 99:

Question 3:

Subtract (2a 3b + 4c) from the sum of (a + 3b − 4c), (4ab + 9c) and (−2b + 3ca).

Answer:

(a + 3b − 4c) + (4ab + 9c) + (−2b + 3ca)
= a + 4a - a + 3b -b -2b -4c +9c + 3c
= 4a + 8c

Now,  (4a + 8c ) - (2a 3b + 4c)
= 4a - 2a + 3b + 8c - 4c
= 2a + 3b + 4c

Page No 99:

Question 4:

Subtract the sum of (8m − 7n + 6p2) and (−3m − 4np2) from the sum of (2m + 4n − 3p2) and (− mn − p2).

Answer:

(8m − 7n + 6p2) + (−3m − 4np2)
 =8m - 3m - 7n -4n + 6p2 - p 2=5m -11n +5p2 

(2m + 4n − 3p2) + (− mn − p2).
 = 2m -m + 4n -n -3p2 -p2=m + 3n -4p2


Now, (m+ 3n - 4p2) - (5m -11n +5p2)=-4m +14n -9p2

Page No 99:

Question 5:

Subtract the sum of (8a − 6a2 + 9) and (−10a − 8 + 8a2) from −3.

Answer:

(8a − 6a2 + 9)+  (−10a − 8 + 8a2)

Collecting like terms and adding them:

 8a -10a -6a2 + 8a2 +9 -8= -2a + 2a2 + 1Now, -3 -(-2a + 2a2 + 1)= 2a - 2a2 -4



Page No 100:

Question 6:

Simplify:

(i) (5x −9y) − (−7x + y)
(ii) x2-x-12x-3+3x2
(iii) [7 − 2x + 5y − (x − y)] − (5x + 3y − 7)
(iv) 13y2-47y+5-27y-23y2+2-17y-3+2y2

Answer:

Collecting like terms and adding them:

(i)  5x + 7x - 9y -y
= 12x -10y

(ii)
x2 -32x2 -x -12x +32=-12x2 - 32x + 32

(iii)  7 + 7 - 2x -x - 5x + 5y + y - 3y
= 14 - 8x -3y

(iv) 
13y2 +23y2 -2y2 - 47y - 27y -17y +5 -2 +3= - y2 - y +6



Page No 102:

Question 1:

Find the products:

3a2 × 8a4

Answer:

3a2 × 8a4
=(3×8)×(a2×a4)=24 ×a(2+4)=24a6

Page No 102:

Question 2:

Find the products:

−6x3 × 5x2

Answer:

−6x3 × 5x2
=(-6×5)×(x3×x2)=(-30)×(x(3+2))=-30x5

Page No 102:

Question 3:

Find the products:

(−4ab) × (−3a2bc)

Answer:

(−4ab) × (−3a2bc)
=(-4×-3)×(a×a2×b×b×c)=12×(a3b2c)= 12a3b2c

Page No 102:

Question 4:

Find the products:

(2a2b3) × (−3a3b)

Answer:

(2a2b3) × (−3a3b)
=(2×(-3))×(a2×a3×b3×b)=(-6)×(a(2+3)×b(3+1))=-6a5b4

Page No 102:

Question 5:

Find the products:

23x2y×35xy2

Answer:

=(23×35)×(x2×x×y×y2))=25×x(2+1)×y(1+2)=25x3y3

Page No 102:

Question 6:

Find the products:

-34ab3×-23a2b4

Answer:

=(-34×-23)×(a×a2×b3×b4)=12×a(1+2)×b(3+4)=12a3b7

Page No 102:

Question 7:

Find the products:

-127a2b2×-92a3bc2

Answer:

=(-127×-92)×(a2×a3×b2×b×c2)=16×a(2+3)×b(2+1)×c2=16a5b3c2

Page No 102:

Question 8:

Find the products:

-135ab2c×73a2bc2

Answer:

=(-135×73)×(a×a2×b2×b×c×c2)=-9115a(1+2)×b(2+1)×c(1+2)=-9115a3b3c3

Page No 102:

Question 9:

Find the products:

-185x2z×-256xz2y

Answer:

=(-185×-256)×(x2×x×z×z2×y)=15×x(2+1)×y×z(1+2)=15x3yz3

Page No 102:

Question 10:

Find the products:

-314xy4×76x3y

Answer:

=(-314×76)×(x×x3×y4×y)=-14x(1+3)×y(4+1)=-14x4y5

Page No 102:

Question 11:

Find the products:

-75x2y×32xy2×-65x3y3

Answer:

=(-75×32×-65)×(x2×x×x3×y×y2×y3)=6325×x(2+1+3)×y(1+2+3)=6325x6y6

Page No 102:

Question 12:

Find the products:

(2a2b) × (−5ab2c) × (−6bc2)

Answer:

=(2×(-5)×(-6))×(a2×a×b×b2×b×c×c2)=60×a(2+1)×b(1+2+1)×c(1+2)=60a3b4c3

Page No 102:

Question 13:

Find the products:

(−4x2) × (−6xy2) × (−3y)

Answer:

=(-4×(-6)×(-3))×(x2×x×y2×y)=-72×x(2+1)×y(2+1)=-72x3y3

Page No 102:

Question 14:

 Find the products:

-35s2t×157st2u×79su2

Answer:

=(-35×157×79)×(s2×s×s×t×t2×u×u2)=-1×s(2+1+1)×t(1+2)×u(1+2)=-s4t3u3

Page No 102:

Question 15:

 Find the products:

-27u4v×-145uv3×-34u2v3

Answer:

=(-27×-145×-34)×(u4×u×u2×v×v3×v3)=-35×u(4+1+2)×v(1+3+3)=-35u7v7

Page No 102:

Question 16:

 Find the products:

(ab2) × (−b2c) × (−a2c3) × (−3abc)

Answer:

=(-3×-1×-1)×(a×a2×a×b2×b2×b×c×c3×c=-3×a(1+2+1)×b(2+2+1)×c(1+4+1)=-3a4b5c5

Page No 102:

Question 17:

 Find the products:

43x2yz×13y2zx×-6xyz2

Answer:

=(43×13×(-6))×(x2×x×x×y×y2×y×z×z×z2)=-83×x(2+1+1)×y(1+2+1)×z(1+1+2)=-83x4y4z4

Page No 102:

Question 18:

Multiply -23a2b by65a3b2 and verify your result for a = 2 and b = 3.

Answer:

-23a2b×65a3b2=(-23×65)×(a2×a3×b×b2)=-45×a(2+3)×b(1+2)=-45a5b3


When a =2 and b =3, we get:

-23a2b = -23×22×3 = -865a3b2= 65×23×32 = 4325L.H.S.=-23a2b ×65a3b2 = -8×4325=-34565R.H.S. = -45a5b3=-45×25×33 = -34565

L.H.S. = R.H.S.

Hence, the result is verified.

Page No 102:

Question 19:

Multiply -821x2y3 by-716xy2 and verify your result for x = 3 and y = 2.

Answer:

-821x2y3 × -716xy2 = -821×-716x2+1y3+2 = 16×x3×y5 When x=3 and y=2, we get:L.H.S.= -821x2y3 ×-716xy2 = -1927×-214= 144R.H.S. = 16x3y5= 16×33×25 = 144L.H.S.= R.H.S.  -821x2y3 ×-716xy2 = 16x3y5

Page No 102:

Question 20:

Find the value of (2.3a5b2) × (1.2a2b2), when a = 1 and b = 0.5.

Answer:

=(2.3×1.2)×(a5×a2×b2×b2)=2.76×a(5+2)×b(2+2)=2.76a7b4When a = 1 and b= 0.5, we get: 2.76a7b4 = 2.76×17×0.54 = 0.1725

Page No 102:

Question 21:

Find the value of (−8u2v6) × (−20uv) for u = 2.5 and v = 1.

Answer:

=(-8×(-20))×(u2×u×v6×v)= 160×u(2+1)×v(6+1)=160u3v7 160u3v7 = 160×2.53×17 = 2500



Page No 103:

Question 22:

Find the product and verify the result for a = 1, b = 2 and c = 3.

25a2b×-15b2ac×-12c2

Answer:

=(25×-15×-12)×(a2×a×b×b2×c×c2)=3×a(2+1)×b(1+2)×c(1+2)=3a3b3c3When a = 1, b = 2 and c = 3, we get:25a2b = 25×12×2= 45-15b2ac = -15×22×1×3= -180-12c2 = -12×32 = -92L.H.S.= 25a2b×-15b2ac×-12c2 = 45×-180×-92 = 648R.H.S.= 3a3b3c3 = 3×13×23×33= 648L.H.S.= R.H.S.  25a2b×-15b2ac×-12c2 =3a3b3c3 

Page No 103:

Question 23:

Find the product and verify the result for a = 1, b = 2 and c = 3.

14abc×-6b2c×-13c3

Answer:

=(14×-6×-13)×(a×b×b2×c×c×c3)=12×a×b(1+2)×c(1+1+3)=12ab3c5When a =1, b = 2 and c = 3, we get:14abc = 14×1×2×3 = 32-6b2c = -6 ×22×3 = -72-13c3= -13×33=-9L.H.S.= 14abc ×-6b2c ×-13c3 = 32×-72×-9 = 972R.H.S. = 12ab3c5 = 12×1×23×35= 972L.H.S. = R.H.S.14abc ×-6b2c ×-13c3 = 12ab3c5

Page No 103:

Question 24:

Find the product and verify the result for a = 1, b = 2 and c = 3.

49abc3×-275a3b2×-8b3c

Answer:

=(49×-275×-8)×(a×a3×b×b2×b3×c3×c)=965×a(1+3)×b(1+2+3)×c(3+1)=965a4b6c4When a=1, b=2 and c=3:L.H.S.: (49×-275×-8)×(a×a3×b×b2×b3×c3×c) =  (49×-275×-8)×1×13×2×22×23×33×3= 4976645R.H.S.: 965a4b6c4 = 96514×26×34 = 4976645L.H.S. = R.H.S.Hence, verified.

Page No 103:

Question 25:

Find the product and verify the result for a = 1, b = 2 and c = 3.

-47a2b×-23b2c×-76c2a

Answer:

=(-47×-23×-76)×(a2×a×b×b2×c×c2)=-49a(2+1)×b(1+2)×c(1+2)=-49a3b3c3L.H.S.: (-47×-23×-76)×(12×1×2×22×3×32)= -96R.H.S.: -49×13×23×33  =  -96L.H.S. = R.H.S. Hence, verified.



Page No 104:

Question 1:

Find the product:

4a(3a + 7b)

Answer:

=4a× 3a + 4a× 7b=4× 3 × a(1+1) + 4× 7 × a× b=12a2 +28ab

Page No 104:

Question 2:

Find the product:

5a(6a − 3b)

Answer:

=5a×6a -5a×3b=5×6×a×a -(5×3×a×b)=30a2-15ab

Page No 104:

Question 3:

Find the product:

8a2(2a + 5b)

Answer:

=8a2×2a +8a2×5b=8×2×a2×a +8×5×a2×b=16a(2+1) +40a2b=16a3+40a2b

Page No 104:

Question 4:

Find the product:

9x2(5x + 7)

Answer:

=9x2×5x +9x2×7=9×5×x2×x + 9×7×x2=45x(2+1) +63x2=45x3+63x2

Page No 104:

Question 5:

Find the product:

ab(a2 b2)

Answer:

=ab×a2-ab×b2=a(1+2)b-ab(1+2)=a3b -ab3

Page No 104:

Question 6:

Find the product:

2x2(3x − 4x2)

Answer:

=2x2×3x -2x2×4x2=2×3×x2×x -2×4×x2×x2=6×x(2+1) -8×x(2+2)=6x3-8x4

Page No 104:

Question 7:

Find the product:

35m2n(m+5n)

Answer:

=35m2n ×m +35m2n×5n=35×m2×m×n+35×5×m2×n×n=35m(2+1)×n +3×m2×n(1+1)=35m3n +3m2n2

Page No 104:

Question 8:

Find the product:

−17x2(3x − 4)

Answer:

=-17x2×3x -(-17x2×4)=-17×3×x2×x +17×4×x2=-51×x(2+1) +68x2=-51x3 +68x2

Page No 104:

Question 9:

Find the product:

72x247x+2

Answer:

=72x2×47×x +72x2×2=72×47×x2×x +72×2×x2=2×x(2+1)+7x2=2x3 +7x2

Page No 104:

Question 10:

Find the product:

−4x2y(3x2 − 5y)

Answer:

=-4x2y ×3x2 -(-4x2y×5y)=-4×3×x2×x2×y + 4×5×x2×y×y=-12×x(2+2)×y +20×x2×y(1+1)=-12x4y +20x2y2

Page No 104:

Question 11:

Find the product:

-427xyz92x2yz-34xyz2

Answer:

=-427xyz×92x2yz -(-427xyz ×34xyz2)=-427×92×x×x2×y×y×z×z +  427×34×x×x×y×y×z×z2=-23×x(1+2) ×y(1+1)×z(1+1) + 19×x(1+1)×y(1+1)×z(1+2)=-23x3y2z2 +19x2y2z3

Page No 104:

Question 12:

Find the product:

9t2(t + 7t3)

Answer:

=9t2×t +9t2×7t3=9×t2×t+9×7×t2×t3=9×t(2+1) +63×t(2+3)=9t3+63t5

Page No 104:

Question 13:

Find the product:

10a2(0.1a − 0.5b)

Answer:

=10a2×0.1a - 10a2×0.5b=10×0.1×a2×a -10×0.5×a2×b=1×a(2+1) -5 a2b=a3 -5a2b

Page No 104:

Question 14:

Find the product:

1.5a(10a2 − 100ab2)

Answer:

=1.5a×10a2b -1.5a×100ab2=1.5×10×a×a2b -  1.5×100×a×a×b2=15×a(1+2)b-150 ×a(1+1)×b2=15a3b-150a2b2

Page No 104:

Question 15:

Find the product:

23abc(a2+b2-3c2)

Answer:

=23abc×a2 +23abc×b2-23abc×3c2=23a×a2×b×c+23a×b×b2×c -23×3×a×b×c×c2=23×a(1+2)×b×c+23×a×b(1+2)×c -2×a×b×c(1+2)=23a3bc +23ab3c -2abc3

Page No 104:

Question 16:

Find the product 24x2(1−2x) and evaluate it for x = 2.

Answer:

   24x2(1−2x)=24x2×1 -24x2×2x=24x2 -24×2×x2×x=24x2-48x3When x =2:L.H.S. = 24x2(1-2x) = 24×22(1-2×2) = 96 (1-4)=96×(-3) = -288R.H.S.=  24x2-48x2  = 24×22 - 48×23 = 96-384 = -288L.H.S.= R.H.S.   24x2(1-2x) = 24x2-48x3

Page No 104:

Question 17:

Find the product ab(a2+b2) and evaluate it for a = 2 and b = 12.

Answer:

ab(2+b2)=ab×a2+ab×b2=a×a2×b +a×b×b2=a(1+2)×b +a×b(1+2)=a3b +ab3When a=2 and b =12, we get:L.H.S.  = ab(a2 +b2) = 2×12(22+122) = 4 +14=174R.H.S.  = a3b +ab3 = 23×12 + 2×123 = 4+ 14 =174  L.H.S. = R.H.S.

Page No 104:

Question 18:

Find the product s (s2 st) and find its value for s = 2 and t = 3.

Answer:

s (s2− st)=s×s2-s×st=s(1+2) -s(1+1)×t=s3-s2tWhen s =2 and t = 3, we get:L.H.S.= s(s2 -st) = 2(22-2×3) = 2 ×(4-6) = -4R.H.S. = s3-s2t = 23-22×3 = 8 - 12 = -4L.H.S.= R.H.S.  s(s2 -st) =  s3-s2t 

Page No 104:

Question 19:

Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.

Answer:

   -3y(xy+y2)=-3y×xy -3y×y2=-3×x×y×y -3×y×y2=-3×x×y(1+1) -3×y(1+2)=-3xy2  -3y3When x = 4 and y =5, we get:L.H.S.= -3y(xy +y2) = -3×5(4×5 + 52) = -15 ×(20 +25) = -675R.H.S. =-3xy2  -3y3 = -3×4×52 -3×53 = -300- 375 =-675L.H.S.= R.H.S. -3y(xy +y2) =  -3xy2  -3y3

Page No 104:

Question 20:

Simplify

a(b − c) + b(c − a) + c(a − b)

Answer:

    a(b − c) + b(c − a) + c(a − b)=a×b -a×c +b×c -b×a +c×a -c×b=ab -ac +bc -ab +ac -bc=0

Page No 104:

Question 21:

Simplify

a(b − c− b(c − a) − c(a − b)

Answer:

    a(b-c)-b (c-a)-c(a-b)=a×b -a×c -b×c+b×a -c×a +c×b=ab +ab -ac - ac -bc +bc=2ab - 2ac=2a(b-c)

Page No 104:

Question 22:

Simplify

3x2 + 2(x + 2) 3x(2x + 1)

Answer:

    3x2 +2(x+2)-3x(2x+1)=3x2 +2×x +2×2 -3x×2x -3x=3x2 +2x +4 -6x2 -3x=-3x2-x +4

Page No 104:

Question 23:

Simplify

x(x + 4) + 3x(2x2 − 1) + 4x2 + 4

Answer:

    x(x+4) +3x(2x2-1) +4x2+4=x×x +x×4 +3x×2x2 -3x +4x2 +4=x(1+1) +4x +6×x(1+2)-3x +4x2+4=x2 +4x +6x3-3x +4x2 +4=6x3+5x2 +x +4

Page No 104:

Question 24:

Simplify

2x2 + 3x(1 − 2x3) + x(x + 1)

Answer:

   2x2 +3x(1-2x3)+x(x+1)=2x2 +3x -3x×2x3 +x2 +x=2x2 +3x -6×x(1+3) +x2+x=2x2+3x -6x4 +x2 +x=-6x4+3x2 +4x

Page No 104:

Question 25:

Simplify

a2b(a b2) + ab2(4ab − 2a2) −a3b(1 − 2b)

Answer:

    a2b(a-b2)+ab2(4ab-2a2) -a3b(1-2b)=a2b×a -a2b×b2 +ab2×4ab -ab2×2a2-a3b +a3b×2b=a(2+1)×b - a2×b(1+2) +4×a(1+1)×b(2+1) -2×a(1+2)×b2-a3b +2×a3×b(1+1)= a3b -a2b3 +4a2b3-2a3b2-a3b +2a3b2=3a2b3

Page No 104:

Question 26:

Simplify

4st(s t) −6s2(tt2) −3t2 (2s2 s) +2st (st)

Answer:

    4st(s-t)-6s2(t-t2)-3t2(2s2-s)+2st(s-t) =4st×s -4st×t -6s2×t-6s2×(-t2) -3t2×2s2-3t2×(-s) +2st×s -2st×t=4×s(1+1)×t -4×s×t(1+1) -6s2t +6s2t2 -6t2s2+3t2s +2×s(1+1)×t -2×s×t(1+1)=4s2t -4st2-6s2t +6s2t2-6t2s2+3t2s+2s2t -2st2=4s2t -6s2t+2s2t -4st2 +3st2-2st2 =-3st2



Page No 106:

Question 1:

Find the product:

(5x + 7)(3x + 4)

Answer:

    (5x+7)(3x+4)=5x×(3x+4)+7×(3x+4)=(5x×3x +5x×4) +(7×3x+7×4)=15x2+20x +21x +28=15x2+41x+28

Page No 106:

Question 2:

Find the product:

(4x − 3)(2x + 5)

Answer:

    (4x-3)(2x+5)=4x×(2x+5) -3×(2x+5)=(4x×2x +4x×5) -(3×2x +3×5)=8x2 +20x -6x-15=8x2+14x -15

Page No 106:

Question 3:

Find the product:

(− 6)(4x + 9)

Answer:

    (x-6)(4x+9)=x×(4x+9) -6×(4x+9)=(x×4x +x×9) -(6×4x +6×9)=4x2 +9x -24x-54=4x2-15x -54

Page No 106:

Question 4:

Find the product:

(5y − 1)(3y − 8)

Answer:

(5y-1)(3y-8) =5y×(3y-8) -1×(3y-8)=(5y×3y -5y×8) -(3y-8)=15y2-40y -3y +8=15y2-43y +8

Page No 106:

Question 5:

Find the product:

(7x + 2y)(x + 4y)

Answer:

(7x+2y)(x+4y)=7x×(x+4y) +2y×(x+4y)=(7x×x +7x×4y) +(2y×x+2y×4y)=7x2+28xy +2xy +8y2=7x2+30xy +8y2

Page No 106:

Question 6:

Find the product:

(9x + 5y)(4x + 3y)

Answer:

(9x+5y)(4x+3y)=9x×(4x+3y) +5y×(4x+3y)=(9x×4x +9x×3y) +(5y×4x +5y×3y)=36x2+27xy+20xy+15y2=36x2+47xy +15y2

Page No 106:

Question 7:

Find the product:

(3m − 4n)(2m − 3n)

Answer:

(3m-4n)(2m-3n)=3m×(2m-3n) -4n×(2m-3n)=(3m×2m -3m×3n) -(4n×2m -4n×3n)=6m2-9mn -8nm +12n2=6m2-17mn +12n2

Page No 106:

Question 8:

Find the product:

(0.8x −  0.5y)(1.5x −  3y)

Answer:

(0.8x-0.5y)(1.5x-3y)=0.8x×(1.5x-3y) -0.5y×(1.5x-3y)=(0.8x×1.5x -0.8x×3y) -(0.5y×1.5x -0.5y×3y)=1.2x2-2.4xy -0.75yx +1.5y2=1.2x2-3.15xy +1.5y2

Page No 106:

Question 9:

Find the product:

15x+2y23x-y

Answer:

15x+2y23x-y=15x×23x -y +2y×23x-y=15x×23x -15x×y +2y×23x -2y×y=215x2-15xy +43yx-2y2=215x2+1715xy -2y2

Page No 106:

Question 10:

Find the product:

25x-12y(10x-8y)

Answer:

(25x-12y)(10x-8y)=25x×(10x-8y) -12y×(10x -8y)=(25x×10x - 25x×8y) -(12y ×10x -12y×8y)=4x2-165xy -5yx +4y2=4x2 -415xy +4y2

Page No 106:

Question 11:

Find the product:

34a+23b(4a+3b)

Answer:

(34a+23b)(4a+3b)=34a×(4a+3b) +23b×(4a+3b)=(34a×4a +34a×3b)+(23b×4a +23b×3b)=3a2 +94ab+83ba +2b2=3a2+5912ab +2b2

Page No 106:

Question 12:

Find the product:

(x2a2)(xa)

Answer:

(x2-a2)(x-a) =x2×(x-a) -a2×(x-a)=(x2×x -x2×a) -(a2×x -a2×a)=x3 -ax2 -a2x +a3

Page No 106:

Question 13:

Find the product:

(3p2 + q2)(2p2 − 3q2)

Answer:

(3p2+q2(2p2-3q2)=3p2×(2p2-3q2) +q2×(2p2-3q2)=(3p2×2p2-3p2×3q2) +(q2×2p2 -q2×3q2)=6p4-9p2q2 +2q2p2 -3q4=6p4 -7p2q2-3q4

Page No 106:

Question 14:

Find the product:

(2x2 − 5y2)(x2 + 3y2)

Answer:

(2x2-5y2)(x2 +3y2) =2x2×(x2 +3y2) -5y2×(x2 +3y2)=(2x2×x2 +2x2×3y2) -(5y2×x2 +5y2×3y2)=2x4 +6x2y2 -5y2x2 -15y4=2x4 +x2y2 -15y4

Page No 106:

Question 15:

Find the product:

(x3y3)(x2 + y2)

Answer:

(x3-y3)(x2+y2)=x3×(x2 +y2) -y3×(x2+y2)=(x3×x2+x3×y2) -(y3×x2 +y3×y2)=x5 +x3y2-x2y3 -y5

Page No 106:

Question 16:

Find the product:

(x4 + y4)(x2 − y2)

Answer:

(x4+y4)(x2 -y2)=x4×(x2 -y2) +y4×(x2-y2)=(x4×x2-x4×y2) +(y4×x2 -y4×y2)=x6-x4y2+x2y4 -y6

Page No 106:

Question 17:

Find the product:

x4+1x4x+1x

Answer:

x4+1x4(x+1x) =x4×(x+1x) +1x4×(x+1x)=(x4×x + x4×1x)+(1x4×x +1x4×1x)=x5+x3+1x3+1x5

Page No 106:

Question 18:

Find the product:

(x2y2)(x + 2y)

Answer:

(x2-y2)(x+2y)=x2×(x+2y) -y2×(x+2y)=(x2×x +x2×2y) -(y2×x +y2×2y)=x3 +2x2y-xy2 -2y3

Page No 106:

Question 19:

Find the product:

(2x + 3y − 5)(x + y)

Answer:

(2x+3y-5)(x+y)=2x×(x+y) +3y×(x+y) -5×(x+y)=(2x×x +2x×y )+(3y×x +3y×y) -(5×x +5×y)=2x2 +2xy +3yx +3y2-5x -5y=2x2 +5xy -5x -5y+3y2

Page No 106:

Question 20:

Find the product:

(3x + 2y − 4)(xy)

Answer:

By column method:

    3x +2y -4      × ( x- y)  3x2 +2yx -4x        -3xy -2y2+4yAdd:  3x2 -xy -4x +4y -2y2  (3x +2y -4)(x-y) = 3x2 -xy -4x +4y -2y2

Page No 106:

Question 21:

Find the product:

(x2 − 3x + 7)(2x + 3)

Answer:

By column method:

     x2-3x +7     ×  (2x+3)     2x3 -6x2+14x              3x2 -9x +21Add:  2x3 -3x2 +5x +21  (x2-3x +7)(2x+3) = 2x3 -3x2 +5x +21

Page No 106:

Question 22:

Find the product:

(3x2 + 5x − 9)(3x −9)

Answer:

By column method:

            3x2 +5x -9            ×  (3x -9)        9x3 +15x2 -27x                                 -27x2 -45x +81     Add:  9x3 -12x2 -72x +81     (3x2 +5x -9)(3x-9) =9x3 -12x2 -72x +81 

Page No 106:

Question 23:

Find the product:

(9x2 x + 15)(x2 − 3)

Answer:

By column method:

            9x2 -x +15           ×     (x2 -3)              9x4-x3 +15x2                                     -27x2 +3x -45      Add:      9x4-x3-12x2+3x -45     (9x2 -x +15)(x2 -3) = 9x4-x3-12x2+3x -45

Page No 106:

Question 24:

Find the product:

(x2 + xy + y2)(xy)

Answer:

By column method:

         x2+xy +y2         ×  (x-y)      x3+x2y +xy2               -x2y -xy2 -y3    Add:    x3 -y3     ( x2+xy +y2 )(x-y) =x3 -y3  

Page No 106:

Question 25:

Find the product:

(x2 xy + y2)(x + y)

Answer:

By column method:

     x2 -xy+y2       × (x+y)    x3-x2y +xy2          x2y -xy2 +y3Add:  x3  +y3 (x2 -xy+y2)(x + y) =x3  +y3

Page No 106:

Question 26:

Find the product:

(x2 − 5x + 8)(x2 + 2)

Answer:

By column method:
              x2-5x +8                 × (x2 +2)            x4 -5x3 +8x2                                         2x2 -10x +16     Add: x4 -5x3 +10x2 -10x +16  (x2-5x +8)(x2+2) = x4 -5x3 +10x2 -10x +16

Page No 106:

Question 27:

Simplify

(3x + 4)(2x − 3) + (5x − 4)(x + 2)

Answer:

(3x +4)(2x -3)
=3x×(2x -3) +4×(2x-3)=6x(1+1) -9x +8x -12=6x2 -x -12(5x-4)(x+2)=5x(x+2) -4(x+2)=5x(1+1) +10x -4x -8=5x2 +6x -8

∴ (3x + 4)(2x − 3) + (5x − 4)(x + 2)

=6x2-x-12 +5x2 +6x -8=11x2 +5x -20

Page No 106:

Question 28:

Simplify

(5x − 3)(x + 4) − (2x + 5)(3x − 4)

Answer:

(5x-3)(x+4)

=5x×(x+4) -3×(x+4)=5x(1+1) +20x -3x -12=5x2+17x -12

(2x +5)(3x-4)

=2x×(3x-4) +5×(3x-4)=6x(1+1) -8x +15x -20=6x2+7x -20

∴ (5x − 3)(x + 4) − (2x + 5)(3x − 4)

=5x2+17x -12 -(6x2 +7x -20)=5x2 -6x2 +17x -7x -12 +20=-x2 +10x +8

Page No 106:

Question 29:

Simplify

(9x − 7)(2x − 5) − (3x − 8)(5x − 3)

Answer:

(9x-7)(2x-5)=9x×(2x-5) -7×(2x-5)=18x(1+1) -45x -14x +35=18x2 -59x +35(3x-8)(5x-3)=3x×(5x-3) -8×(5x-3)=15x2 -9x -40x +24=15x2-49x +24  (2x − 5) − (3x − 8)(5x − 3)=18x2 -59x +35 -(15x2-49x +24)=18x2-15x2 -59x +49x +35 -24=3x2 -10x +11

Page No 106:

Question 30:

Simplify

(2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

Answer:

(2x +5y)(3x+4y)

=2x×(3x+4y) +5y×(3x+4y)=6x(1+1) +8xy +15yx +20y(1+1)=6x2 +23xy +20y2(7x +3y)(2x +y)=7x(2x +y) +3y(2x +y)=14x(1+1) +7xy +6yx +3y(1+1)=14x2 +13xy+3y2

∴ (2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

=6x2+23xy +20y2 -(14x2 +13xy +3y2)=6x2 -14x2 +23xy -13xy +20y2 -3y2=-8x2 +10xy +17y2

Page No 106:

Question 31:

Simplify

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

Answer:

(3x2 + 5x − 7)(x − 1)

By column method:

            3x2 +5x -7              × (x -1)       3x3 +5x2 -7x                          -3x2 -5x +7   Add:   3x3 +2x2 -12x+7  


(x2 − 2x + 3)(x + 4)

By column method:

                x2 -2x +3               ×  (x +4)         x3 -2x2 +3x                      4x2 -8x +12  Add:    x3 +2x2 -5x +12

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

=3x3 +2x2 -12x +7 -(x3+2x2 -5x +12)=3x3-x3 +2x2 -2x2 -12x +5x +7 -12=2x3 -7x -5



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