Question

Factorise 9x2-12ax-y2-z2-2yz+4a2

Answer 1

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Answer 2

The required factorization is $(3x-2a+y+z)(3x-2a-y-z)$.

Step-by-step explanation:

Consider the provided expression.

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

Rearrange the terms.

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

$[(3x)^{2}-2\times 3x\times 2a+(2a)^{2}]-(y^{2}+z^{2}+2\times y\times z)$

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

Use the formula: $a^2-b^2=(a+b)(a-b)$

$[(3x-2a)+(y+z)][(3x-2a)-(y+z)]$

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

The required factorization is $(3x-2a+y+z)(3x-2a-y-z)$.

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