Question

X 2 +4y 2 +9z 2 -4xy+12yz-6zx

Answer 1

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Answer 2

Answer:

$\red{x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx}$

$\green{=(-x+2y+3z)(-x+2y+3z)}$

Step-by-step explanation:

$Given \: x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx$

$= (-x)^{2} + (2y)^{2}+(3z)^{2}+2\times (-x)\times 2y+2\times 2y\times 3z+2\times 3z\times (-x)$

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

$\boxed {\pink { Since,\:a^{2}+b^{2}+c^{2}+2ab+2bc+2ca = (a+b+c)^{2}}}$

Therefore.,

$\red{x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx}$

$\green{=(-x+2y+3z)(-x+2y+3z)}$

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