Question

4x$4x^{2} +9y^{2} +16z^{2} +12xy-24yz-16xz$

Answer 1

Question:-

4x² + 9y² + 16z² + 12xy – 24yz – 16xz.

Given:-

4x² + 9y² + 16z² + 12xy – 24yz – 16xz.

To Find:-

Factorize the given function:

4x² + 9y² + 16z² + 12xy – 24yz – 16xz.

Solution:-

We know 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).

Answer:-

${ \boxed{ \sf \large \color{gold}4x {}^{2} + 9y {}^{2} + 16z {}^{2} + 12xy - 24yz - 16xz = (2x + 3y - 4z) {}^{2} }}$

Hope you have satisfied. ⚘