Question

Factorize a(a+b)^3 -3a^2b(a+b)​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

Given : a(a + b)³ - 3a²b(a + b)

Here  a(a + b) is a common factor :

= a(a + b) {(a + b)² – 3ab}

By Using Identity : (a + b)²  = a² + b² + 2ab :

= a(a + b) {a² + b² + 2ab – 3ab}

= a(a + b) (a² + b² – ab)

a(a + b)³ - 3a²b(a + b)= a(a + b) (a² + b² – ab)

 Hence, the factorisation of a(a + b)³ - 3a²b(a + b) is  a(a + b) (a² + b² – ab).

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