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Algebraic Identities

Factorise: ...

Question

Factorise: $9 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 4 a^{2}$

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Solution

$9 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 4 a^{2}$
$9 x^{2} - 12 a x + 4 a^{2} - (y^{2} + 2 y z + z^{2})$
$(3 x)^{2} - 12 a x + (2 a)^{2} - (y + z)^{2}$
$(3 x - 2 a)^{2} - (y + z)^{2}$
$\Rightarrow (3 x - 2 a + y + z) (3 x - 2 a - y - z)$

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9 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 4 a^{2}

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