Factorise ${(4 x + y)}^{2} + (4 x + y) (x + 2 y) - 20 {(x + 2 y)}^{2}$ .

(9 x + 11 y) (x + 9 y)

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- (9 x + 11 y) (x - 9 y)

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- (9 x + 11 y) (7 y)

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(9 x - 11 y) (x - 9 y)

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Solution

The correct option is C $- (9 x + 11 y) (7 y)$
${(4 x + y)}^{2} + (4 x + y) (x + 2 y) - 20 {(x + 2 y)}^{2}$ .
We know, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$

$\Rightarrow$ $16 x^{2} + 8 x y + y^{2} + 4 x^{2} + 8 x y + x y + 2 y^{2} - 20 (x^{2} + 4 x y + 4 y^{2})$

$\Rightarrow$ $20 x^{2} + 17 x y + 3 y^{2} - 20 x^{2} - 80 x y - 80 y^{2}$

$\Rightarrow$ $- 63 x y - 77 y^{2}$

$\Rightarrow$ $(7 y) (- 9 x - 11 y)$

$\Rightarrow$ $- (9 x + 11 y) (7 y)$

Suggest Corrections

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