Factorise: $16 {(2 x - y)}^{2} - 24 (4 x^{2} - y^{2}) + {9 (2 x + y)}^{2}$

(2 x - 7 y) (2 x + 7 y)

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(2 x + 7 y) (2 x - 7 y)

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(2 x - 7 y) (2 x - 7 y)

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(2 x + 7 y) (x + 7 y)

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Solution

The correct option is C $(2 x - 7 y) (2 x - 7 y)$
As given $16 {(2 x - y)}^{2} - 24 (4 x^{2} - y^{2}) + {9 (2 x + y)}^{2}$
$\Rightarrow {(4 (2 x - y))}^{2} - 2 \times 4 (2 x - y) \times 3 (2 x + y) + {(3 (2 x + y))}^{2}$
$∵ a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$
$\Rightarrow {[4 (2 x - y) - 3 (2 x + y)]}^{2}$
$\Rightarrow {[8 x - 4 y - 6 x - 3 y]}^{2}$
$\Rightarrow (2 x - 7 y) (2 x - 7 y)$

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Similar questions

Factorise $(2 x - y)^{2} - 14 x + 7 y - 18$

{(2 x - y)}^{2} - 14 x + 7 y - 18

5 (2 x + y)^{2} - (2 x + y) (x - 7 y)

9 x^{2} - 16 y^{2} = 144

x^{2} + y^{2} = 9

y^{2} + 7 y - 144

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