Question

Factorize a(a + b)3 – 3a2b(a + b)​

Answer 1

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

Given :

The expression a(a + b)³ - 3a²b(a + b)

To find :

To factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

a(a + b)³ - 3a²b(a + b)

Step 2 of 2 :

Factorise the expression

a(a + b)³ - 3a²b(a + b)

= a[(a + b)³ - 3ab(a + b)]

= a(a³ + b³) [ ∵ a³ + b³ = (a + b)³ – 3ab(a + b) ]

= a(a + b)(a² – ab + b²) [ ∵ a³ + b³ = (a + b)(a² – ab + b² ) ]

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

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Answer 2

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

Given :

The expression a(a + b)³ - 3a²b(a + b)

To Find :

To factorize the given expression.

Solution :

Factorize the expression

a(a + b)³ - 3a²b(a + b)

= a[(a + b)³ - 3ab(a + b)]

= a(a³ + b³) [ ∵ a³ + b³ = (a + b)³ – 3ab(a + b) ]

= a(a + b)(a² – ab + b²) [ ∵ a³ + b³ = (a + b)(a² – ab + b² ) ]

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