Question

Factorize: a(a+b)^3-3a^2b(a+b)

Answer 1

Answer:

After factorisation,tge given expression becomes

$a(a + b)(a {}^{2} + {b}^{2} - ab)$

Step-by-step explanation:

The given expression is

$a(a + b) {}^{3} - 3 {a}^{2}b(a + b)$

Taking (a+b) as common term we get

$= > (a + b)[a(a + b) {}^{2} - 3 {a}^{2}b ] \\ = (a + b)[a(a {}^{2} + b {}^{2} + 2ab) - 3 {a}^{2} b ] \\ = (a + b)[ {a}^{3} + ab {}^{2} + 2 {a}^{2} b - 3 {a}^{2} b ] \\ = (a + b)[ {a}^{3} + ab {}^{2} - {a}^{2} b ] \\ = (a + b)[ {a}^{3} + ab(b - a) ]$

Taking a as common in second term we get

$= > (a + b)[a(a {}^{2} + b {}^{2} - ab) ] \\ = a(a + b)(a {}^{2} + {b}^{2} - ab)$

Therefore,After factorisation the given expression becomes

$a(a + b)(a {}^{2} + {b}^{2} - ab)$

#SPJ3