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Page No 30:

Question 1:

Factorise.
(1) x2 + 9x + 18
(2) x2 − 10x + 9
(3) y2 + 24y + 144
(4) 5y2 + 5y − 10
(5) p2 − 2p − 35
(6) p2 − 7p − 44
(7) m2 − 23m + 120
(8) m2 − 25m + 100
(9) 3x2 + 14x + 15
(10) 2x2 + x − 45
(11) 20x2 − 26x + 8
(12) 44x2 x − 3

Answer:


1 x2+9x+18=x2+6x+3x+18=xx+6+3x+6=x+3x+6 
2 x2-10x+9=x2-9x-x+9=xx-9-1x-9=x-1x-9
3 y2+24y+144= y2+12y+12y+144= yy+12+12y+12= y+12y+12
4 5y2+5y-10= 5y2+10y-5y-10= 5yy+2-5 y+2=5y-5y+2=5y-1y+2
5 p2-2p-35=p2-7p+5p-35=pp-7+5p-7=p+5p-7
6 p2-7p-44= p2-11p+4p-44=pp-11+4p-11=p+4 p-11
7 m2-23m+120=m2-15m-8m+120=mm-15-8m-15=m-8m-15
8 m2-25m+100=m2 -20m-5m+100=mm-20-5m-20=m-5m-20
9 3x2+14x+15=3x2+9x+5x+15=3xx+3+5x+3=3x+5x+3
10 2x2+x-45= 2x2+10x-9x-45= 2xx+5-9x+5=2x-9x+5
11 20x2-26x+8=20x2-16x-10x+8=4x5x-4-25x-4=4x-25x-4=22x-15x-4
12 44x2-x-3= 44x2+11x-12x-3=11x4x+1-34x+1=11x-34x+1



Page No 31:

Question 1:

Factorise.
(1) x3 + 64y3
(2) 125p3 + q3
(3) 125k3 + 27m3
(4) 2l3 + 432m3
(5) 24a3 + 81b3
(6) y3 + 18y3
(7) a3 + 8a3
(8) 1 + q3125

Answer:

It is known that,
a3+b3=a+ba2+b2-ab
1 x3+64y3=x3+4y3=x+4yx2+4y2-x×4y=x+4yx2+16y2-4xy
2 125p3+q3=5p3+q3=5p+q5p2+q2-5p×q=5p+q25p2+q2-5pq
3 125k3+27m3=5k3+3m3=5k+3m5k2+3m2-5k×3m=5k+3m25k2+9m2-15km
4 2l3+432m3=2l3+216m3=2l3+6m3=2l+6ml2+6m2-l×6m=2l+6m l2+36m2-6lm
5 24a3+81b3=38a3+27b3=32a3+3b3=32a+3b2a2+3b2-2a×3b=32a+3b4a2+9b2-6ab
6 y3+18y3=y3+12y3=y+12yy2+ 12y2-y×12y=y+12yy2+14y2-12
7 a3+8a3=a3+2a3=a+2aa2+2a2-a×2a=a+2a a2+4a2-2
8 1+q3125=13+q53=1+q512+q52-1×q5=1+q51+q225-q5



Page No 32:

Question 1:

Factorise:
(1) y3 − 27
(2) x3 − 64y3
(3) 27m3 − 216n3
(4) 125y3 − 1
(5) 8p3 27p3
(6) 343a3 − 512b3
(7) 64x3 − 729y3
(8) 16a3 128b3

Answer:

It is known that,
a3-b3 = a-ba2+b2+ab
1 y3-27= y3-33=y-3y2+32+y×3=y-3 y2+9+3y
2 x3-64y3=x3-4y3=x-4yx2+4y2+x×4y=x-4yx2+16y2+4xy
3 27m3-216n3=27m3-8n3=27m3-2n3=27m-2nm2+2n2+m×2n=27m-2nm2+4n2+2mn
4 125y3-1=5y3-13=5y-15y2+12+5y×1=5y-125y2+1+5y
5 8p3-27p3=2p3-3p3=2p-3p2p2+3p2+2p×3p=2p-3p4p2+9p2+6
6 343a3-512b3=7a3-8b3=7a-8b7a2+8b2+7a×8b=7a-8b49a2+64b2+56ab
7 64x3-729y3=4x3-9y3=4x-9y4x2+9y2+4x×9y=4x-9y16x2+81y2+36xy
8 16a3-128b3=16a3-8b3=16a3-2b3=16a-2ba2+2b2+a×2b=16a-2ba2+4b2+2ab

Page No 32:

Question 2:

Simplify:
(1) (x + y)3 − (x y)3
(2) (3a + 5b)3 − (3a − 5b)3
(3) (a + b)3 a3 b3
(4) p3 − (p + 1)3
(5) (3xy − 2ab)3 − (3xy + 2ab)3

Answer:

It is known that,
a3-b3=a-ba2+b2+ab
1 x+y3-x-y3=x+y-x-yx+y2+x-y2+x+yx-y=2yx2+y2+2xy+x2+y2-2xy+x2-y2=2y3x2+y2
2 3a+5b3-3a-5b3=3a+5b-3a-5b3a+5b2+3a-5b2+3a+5b3a-5b=10b9a2+25b2+30ab+9a2+25b2-30ab+9a2-25b2=10b27a2+25b2
3 a+b3-a3-b3=a+b3-a3+b3=a+b3-a+ba2+b2-ab=a+ba+b2-a2+b2-ab=a+ba2+b2+2ab-a2-b2+ab=a+b3ab=3a2b+3ab2
4 p3-p+13=p-p+1p2+p+12+p×p+1=-1p2+p2+1+2p+p2+p=-13p2+3p+1=-3p2-3p-1
5 3xy-2ab3-3xy+2ab3=3xy-2ab-3xy+2ab3xy-2ab2+3xy+2ab2+3xy-2ab3xy+2ab=-4ab9x2y2+4a2b2-12abxy+9x2y2+4a2b2+12abxy+9x2y2-4a2b2=-4ab27x2y2+4a2b2=-108x2y2ab-16a3b3



Page No 33:

Question 1:

Simplify:
(1) m2-n2m+n2×m2+mn+n2m3-n3

(2) a2+10a+21a2+6a-7×a2-1a+3

(3) 8x3-27y34x2-9y2

(4) x2-5x-24x+3x+8×x2-64x-82

(5) 3x2-x-2x2-7x+12÷3x2-7x-6x2-4

(6) 4x2-11x+616x2-9

(7) a3-275a2-16a+3÷a2+3a+925a2-1

(8) 1-2x+x21-x3×1+x+x21+x

Answer:

It is known that,
a2-b2=a+ba-b ; a3-b3=a-ba2+ab+b2
1 m2-n2m+n2×m2+mn+n2m3-n3= m+nm-nm+nm+n×m2+mn+n2m-nm2+mn+n2= 1m+n
2 a2+10a+21a2+6a-7×a2-1a+3=a2+7a+3a+21a2+7a-a-7 × a+1a-1a+3= aa+7+3a+7a a+7-1a + 7×a+1a-1a+3= a+7a+3a-1a+7×a+1a-1a+3= a+1
3 8x3-27y34x2-9y2=2x3-3y32x2-3y2= 2x-3y2x2+ 2x×3y+3y22x+3y2x-3y= 2x-3y4x2+6xy+9y22x+3y2x-3y=4x2+ 6xy+9y22x+3y
4 x2-5x-24x+3x+8×x2-64x-82=x2-8x+3x-24x+3x+8×x2-82x-82=xx-8+3x-8 x+3x+8×x+8x-8x-8x-8=x+3x-8x+3x+8×x+8x-8x-8x-8=1
5 3x2-x-2x2-7x+12÷3x2-7x-6x2-4=3x2-3x+2x-2x2-4x-3x+12 ÷ 3x2-9x+2x-6x2-22=3xx-1+2x-1xx-4-3x-4÷3xx-3+2x-3x+2x-2=3x+2x-1x-3x-4÷3x+2x-3x+2x-2=3x+2x-1x-3x-4×x+2x-23x+2x-3=x-1x+2x-2x-4x-3x-3
6 4x2-11x+616x2-9=4x2-8x-3x+64x2-32=4xx-2-3x-24x+34x-3=4x-3x-24x+34x-3=x-24x+3
7 a3-275a2-16a+3÷a2+3a+925a2-1=a3-335a2-15a-a+3 ÷ a2+3a+95a2-12=a-3a2+a×3+325aa-3-1a-3÷a2+3a+95a+15a-1=a-3a2+3a+95a-1a-3÷a2+3a+95a+15a-1=a-3a2+3a+95a-1a-3×5a+15a-1a2+3a+9=5a+1
8 1-2x+x21-x3×1+x+x21+x=1-x-x+x213-x3×1+x+x21+x=11-x-x1-x1-x12+1×x+x2 × 1+x+x21+x=1-x1-x1-x1+x+x2×1+x+x21+x=1-x1+x



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