Question

Factorise:- 4x² + 9y² + 16z² + 12xy – 24yz – 16xz

Answer 1

It is known that,

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

4x2+9y2+16z2+12xy–24yz–16xz

=(2x)²+(3y)²+(−4z)² + 2(2x)(3y) + 2(3y)(−4z) + 2(−4z)(2x)

=(2x+3y–4z)²

=(2x+3y–4z)(2x+3y–4z)