Factorize the equation $4 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 9 a^{2}$

(2 x - 3 a + y) (2 x - 3 a - y - z)

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(2 x - 3 a + y + z) (2 x - 3 a - y - z)

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(3 a + y + z) (2 x - 3 a - y - z)

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(2 x - 3 a + y z) (2 x - a - y - z)

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Solution

The correct option is B $(2 x - 3 a + y + z) (2 x - 3 a - y - z)$
$4 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 9 a^{2}$
$= (4 x^{2} - 12 x a + 9 a^{2}) - (y^{2} + 2 y z + z^{2})$
$= [(2 x) - (2 \times 2 x \times 3 a) + (3 a)^{2}] - [(y)^{2} + 2 y z + (z)^{2}]$
$= (2 x - 3 a)^{2} - (y + z)^{2}$
Using,
$a^{2} - b^{2} = (a + b) (a - b)$
$= (2 x - 3 a + y + z) (2 x - 3 a - y - z)$

Suggest Corrections

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