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

(a + b) (7 a^{2} + 13 a b + 13 b^{2})

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(a - 2 b) (7 a^{2} + 17 a b + 13 b^{2})

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(a - b) (7 a^{2} + 13 a b + 17 b^{2})

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(2 a - b) (7 a^{2} + 17 a b + 17 b^{2})

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Solution

The correct option is B $(a - 2 b) (7 a^{2} + 17 a b + 13 b^{2})$
$(2 a + b)^{3} - (a + 3 b)^{3}$
$= (2 a + b - a - 3 b) [(2 a + b)^{2} + (2 a + b) (a + 3 b) + (a + 3 b)^{2}]$
$= (a - 2 b) (4 a^{2} + 4 a b + b^{2} + 2 a^{2} + 6 a b + a b + 3 b^{2} + a^{2} + 6 a b + 9 b^{2})$
$= (a - 2 b) (7 a^{2} + 17 a b + 13 b^{2})$

Suggest Corrections

Similar questions

2 a^{2} + 13 a b - 24 b^{2}

Factorise : $2 a^{2} - 17 a b + 26 b^{2}$

-

y^{2} = 4 a x

(5 a, 2 a)

Factorise :

(a + b)³ - 8

My attempt

= (a + b)³- (2)³

= (a + b - 2) {(a + b)²+ (2)² + 2(a + b)}

What should I do not?

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