Mathematics Solutions Solutions for Class 8 Math Chapter 5 Expansion Formulae are provided here with simple step-by-step explanations. These solutions for Expansion Formulae are extremely popular among Class 8 students for Math Expansion Formulae Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 5 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 24:

Question 1:

Expand
(1) (a+2)(a−1)
(2) (m−4)(m+6)
(3) (p+8)(p−3)
(4) (13+x)(13−x)
(5) (3x+4y)(3x+5y)
(6) (9x−5t)(9x+3t)
(7) m+23m73
(8) x+1xx1x
(9) 1y+41y9

Answer:

It is known that,
x+ax+b=x2+a+bx+ab
1 a+2a-1=a2+2+-1a+2×-1=a2+2-1a-2=a2+a-2
2 m-4m+6=m2+-4+6m+-4×6=m2+-4+6m-24=m2+ 2m-24
3 p+8p-3=p2+8+-3p+8×-3=p2+8-3p-24=p2+5p-24
4 13+x13-x=-x+13x-13=-x2+13+-13x+13×-13=-x2+13-13x-169=-x2-169=169-x2
5 3x+4y3x+5y=3x2+4y+5y3x+4y×5y=9x2+9y×3x+20y2=9x2+27xy+20y2
6 9x-5t9x+3t=9x2+-5t+3t9x+-5t×3t=81x2+-2t9x-15t2=81x2-18xt-15t2
7 m+23m-73=m2+23+-73m+23×-73=m2+23-73m-149=m2-5m3-149
8 x+1xx-1x=x2+1x+-1xx+1x×-1x=x2+1x-1xx-1x2=x2-1x2
9 1y+41y-9=1y2+4+-91y+4×-9=1y2+-5×1y-36=1y2-5y-36



Page No 25:

Question 1:

Expand
(1) k+43
(2) 7x + 8y3
(3) 7 +m3
(4) 523
(5) 1013
(6) x+1x3
(7) 2m + 153
(8) 5xy+y5x3

Answer:

It is known that,
a+b3=a3+b3+3a2b+3ab2
1 k+43=k3+43+3×k2×4+3×k×42=k3+64+12k2+48k
2 7x+8y3=7x3+8y3+3×7x2×8y+3×7x×8y2=343x3+512y3+1176x2y+1344xy2
3 7+m3=73+m3+3×72×m+3×7×m2=343+m3+147m+21m2
4 523=50+23=503+23+3×502×2+3×50×22=125000+8+15000+600=140608
5 1013=100+13=1003+13+3×1002×1+3×100×12=1000000+1+30000+300=1030301
6 x+1x3=x3+1x3+3×x2×1x+3×x×1x2=x3+1x3+3x+3x
7 2m+153=2m3+153+3×2m2×15+3×2m×152=8m3+1125+12m25+6m25
8 5xy+y5x3=5xy3+y5x3+3×5xy2×y5x+3×5xy×y5x2=125x3y3+y3125x3+15xy+3y5x



Page No 27:

Question 1:

Expand
(1) (2m − 5)3
(2) (4 − p)
(3) (7x − 9y)3
(4) (58)3
(5) (198)3
(6) 2p  12p3
(7) 1  1a3
(8) x3  3x3

Answer:

It is known that,
a-b3=a3-b3-3a2b+3ab2
1 2m-53=2m3-53-3×2m2×5+3×2m×52=8m3-125-60m2+150m
2 4-p3=43-p3-3×42×p+3×4×p2=64-p3-48p+12p2
3 7x-9y3=7x3-9y3-3×7x2×9y+3×7x×9y2=343x3-729y2-1323x2y+1701xy2
4 583=60-23=603-23-3×602×2+3×60×22=216000-8-21600+720=195112
5 1983=200-23=2003-23-3×2002×2+3×200×32=8000000-8-240000+5400=7765392
6 2p-12p3=2p3-12p3-3×2p2×12p+3×2p×12p2=8p3-18p3-6p+32p
7 1-1a3=13-1a3-3×12×1a+3×1×1a2=1-1a3-3a+3a2
8 x3-3x3=x33-3x3-3×x32×3x+3×x3×3x2=x327-27x3-x+9x

Page No 27:

Question 2:

Simplify
(1) (2a + b)3 − (2a − b)3
(2) (3r − 2k)3 + (3r + 2k)3
(3) (4a − 3)3 − (4a +3)3
(4) (5x − 7y)3 + (5x + 7y)3

Answer:

It is known that,
a+b3=a3+b3+3a2b+3ab2;a-b3=a3-b3-3a2b+3ab2 
1 2a+b3-2a-b3=2a3+b3+3×2a2×b+3×2a×b2-2a3-b3-3×2a2×b+3×2a×b2=8a3+b3+12a2b+6ab2-8a3+b3+12a2b-6ab2=2b3+24a2b
2 3r-2k3+3r+2k3=3r3-2k3-3×3r2×2k+3×3r×2k2+3r3+2k3+3×3r2×2k+3×3r×2k2=27r3-8k3-54r2k+36rk2+27r3+8k3+54r2k+36rk2=54r3+72rk2
3 4a-33-4a+33=4a3-33-3×492×3+3×49×32-493+33+3×492×3+3×49×32=64a3-27-144a2+108-64a3-27-144a2-108=-54-288a2
4 5x-7y3+5x+7y3=5x3-7y3-3×5x2×7y+3×5x×7y2+5x3+7y3+3×5x2×7y+3×5x×7y2=125x3-343y3-525x2y+735xy2+125x3+343y3+525x2y+735xy2=250x3+1470xy2



Page No 28:

Question 1:

Expand.
(1) (2p + q +5)2
(2) (m + 2n +3r)2
(3) (3x +4y − 5p)2
(4) (7m − 3n − 4k)2

Answer:

It is known that,
a+b+c2=a2+b2+c2+2ab+2bc+2ca
1 2p+q+52=2p2+q2+52+2×2p×q+2×q×5+2×5×2p=4p2+q2+25+4pq+10q+20p
2 m+2n+3r2=m2+2n2+3r2+2×m×2n+2×2n×3r+2×3r×m=m2+4n2+9r2+4mn+12nr+6mr
3 3x+4y-5p2=3x2+4y2+-5p2+2×3x×4y+2×4y×-5p+2×-5p×3x=9x2+16y2+25p2+24xy-40yp-30px
4 7m-3n-4k2=7m2+-3n2+-4k2+2×7m×-3n+2×-3n×-4k+2×-4k×7m=49m2+9n2+16k2-42mn+24nk-56km

Page No 28:

Question 2:

Simplify.
(1) (x − 2y +3)2 + (x + 2y − 3)2
(2) (3k − 4r − 2m)2 − (3k + 4r − 2m)2
(3) (7a − 6b + 5c)2 + (7a + 6b − 5c)2

Answer:

It is known that,
a+b+c2=a2+b2+c2+2ab+2bc+2ca
1 x-2y+32+x+2y-32=x2+-2y2+32+2×x×-2y+2×-2y×3+2×3×x+x2+2y2+-32+2×x×2y+2×2y×-3+2×-3×x=x2+4y2+9-4xy-12y+6x+x2+4y2+9+4xy-12y-6x=2x2+8y2+18-24y
2 3k-4r-2m2-3k+4r-2m2=3k2+-4r2+-2m2+2×3k×-4r+2×-4r×-2m+2×-2m×3k-3k2+4r2+-2m2+2×3k×4r+2×4r×-2m+2×-2m×3k=9k2+16r2+4m2-24kr+16rm-12mk-9k2-16r2-4m2-24kr+16rm+12mk=32rm-48kr
3 7a-6b+5c2+7a+6b-5c2=7a2+-6b2+5c2+2×7a×-6b+2×-6b×5c+2×5c×7a+7a2+6b2+-5c2+2×7a×6b+2×6b×-5c+2×-5c×7a=49a2+36b2+25c2-84ab-60bc+70ca+49a2+36b2+25c2+84ab-60bc-70ca=98a2+72b2+50c2-120bc



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