Question

Factorise the following:
(2a + b)^3 + (a + 2b)^3

Answer 1

Required Answer:-

Given To Factorise:

• (2a + b)³ + (a + 2b)³

Solution:

We know that,

→ x³ + y³ = (x + y)(x² - xy + y²)

So, if x = 2a + b and y = 2b + a, then,

x³ + y³

= (x + y)(x² - xy + y²)

Substituting the values, we get,

= [(2a + b) + (2b + a)][(2a + b)² - (2a + b)(2b + a) + (2b + a)²]

= [3a + 3b][ (4a² + 4ab + b²) - {2a(2b + a) + b(2b + a)} + (4b² + 4ab + a²)]

= (3a + 3b)[(5a² + 5b² + 8ab) - (4ab + 2a² + 2b² + ab)]

= (3a + 3b)[5a² + 5b² + 8ab - 2a² - 2b² - 5ab]

= 3(a + b)(3a² + 3b² + 3ab)

= 3(a + b) × 3(a² + ab + b²)

= 9(a + b)(a² + ab + b)²

→ Therefore, the factorised form is 9(a + b)(a² + ab + b²)

Answer:

• The factorised form is 9(a + b)(a² + ab + b²)

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