Advertisements
Advertisements
Question
Factorize the following expressions:
(a + b)3 – 8(a – b)3
Advertisements
Solution
(a + b)3 - 8(a - b)3
= (a + b)3 - [2(a - b)]3
= (a + b)3 - (2a - 2b)3 [Using a3 - b3 = (a - b)(a2 + ab + b2 ) ]
= (a + b - (2a - 2b))((a + b)2 + (a + b)(2a - 2b) + (2a - 2b)2)
= (a + b - 2a + 2b)(a2 + b2 + 2ab + (a + b)(2a - 2b) + (2a - 2b)2) [∵ (a + b)2 = a2 + b2 + 2ab]
= (3b - a)(a2 + b2 + 2ab + 2a2 - 2ab + 2ab - 2b2 + (2a - 2b)2)
= (3b - a)(3a2 + 2ab - b2 + (2a - 2b)2 )
= (3b - a)(3a2 + 2ab - b2 + 4a2 + 4b2 - 8ab) [∵ (a - b)2 = a2 + b2 - 2ab]
= (3b - a )(3a2 + 4a2 - b2 + 4b2 + 2ab - 8ab)
= (3b - a )(7a2 + 3b2 - 6ab)
∴ (a + b)3 - 8(a - b)3 = (-a + 3b)(7a2 - 6ab + 3b2)
APPEARS IN
RELATED QUESTIONS
Factorize the following expressions:
y3 +125
Factorize the following expressions:
54x6y + 2x3y4
Factorize the following expressions:
x6 + y6
Factorize 8x2 + y3 +12x2 y + 6xy2
Factorize a3 x3 - 3a2bx2 + 3ab2 x - b3
a3 + 8b3 + 64c3 - 24abc
x3 - 8y3 + 27z3 +18xyz
Write the value of \[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .\]
The value of \[\frac{(0 . 013 )^3 + (0 . 007 )^3}{(0 . 013 )^2 - 0 . 013 \times 0 . 007 + (0 . 007 )^2}\] is
Divide: 6x3 + 5x2 − 21x + 10 by 3x − 2
