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Product of (x+y) (x-y)

Factorise the...

Question

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$9 x^{2} - (3 y + z)^{2}$

A

(3 x + 3 y + z) (- 3 x - 3 y - z)

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B

(3 x + 3 y + z) (3 x - 3 y + z)

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C

(3 x + 3 y + z) (3 x + 3 y - z)

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D

(3 x + 3 y + z) (3 x - 3 y - z)

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Solution

The correct option is D $(3 x + 3 y + z) (3 x - 3 y - z)$
$9 x^{2} - (3 y + z)^{2} = (3 x)^{2} - (3 y + z)^{2} = [3 x + (3 y + z)] [3 x - (3 y + z)] = (3 x + 3 y + z) (3 x - 3 y - z)$

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