Question

Factorise x^2+4y^2+9z^2-4xy+12yz-6zx

Answer 1

Answer:

$Givenx2+4y2+9z2−4xy+12yz−6zx</p><p></p><p>= (-x)^{2} + (2y)^{2}+(3z)^{2}+2\times (-x)\times 2y+2\times 2y\times 3z+2\times 3z\times (-x)=(−x)2+(2y)2+(3z)2+2×(−x)×2y+2×2y×3z+2×3z×(−x)</p><p></p><p>= (-x+2y+3z)^{2}=(−x+2y+3z)2</p><p></p><p>\boxed {\pink { Since,\:a^{2}+b^{2}+c^{2}+2ab+2bc+2ca = (a+b+c)^{2}}}Since,a2+b2+c2+2ab+2bc+2ca=(a+b+c)2</p><p></p><p>Therefore.,</p><p></p><p>\red{x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx}x2+4y2+9z2−4xy+12yz−6zx</p><p></p><p>\green{=(-x+2y+3z)(-x+2y+3z)}=(−x+2y+3z)(−x+2y+3z)</p><p></p><p>•••♪</p><p></p><p>$