Question

3. x2 + 4y2 +972 - 4xy + 12yz - 6zx​

Answer 1

$\small\sf \bf \pink{(-x+2y-3z)(-x+2y-3z)\:}$

Step-by-step explanation:

Correction:

x² +4y² + 9z² - 4xy + 12yz - 6zx

$\small\sf \bf \red{Solution:\:}$

$= (-x)² + (2y)² + (3z)² + 2×(-x)×2y + 2×2y×3z + 2×3z×(-x)$

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

$\mathbb\fcolorbox{purple} {lavenderblush}{Since, a² + b² + c² + 2ab + 2bc + 2ca = (a+b+c)²}$

$\small\sf \bf \blue{x² +4y² + 9z² - 4xy + 12yz - 6zx\:}$

= $\small\sf \bf \pink{(-x+2y-3z)(-x+2y-3z)\:}$