Question

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

Answer 1

The answer is :-

${(4x - 2y + 3z)}^{2} \\ \\ = (4x - 2y + 3z)(4x - 2y + 3z)$


Please refer the above photograph for the used process.



KEY POINTS TO REMEMBER :-


☸️ Some Algebraic identities.
The question uses the formula of :-

${(x + y + z)}^{2}$

The identity can be expanded as follows :-

${x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx \\ \\ = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx)$


Using this identity, we can easily solve the question.


Thanks!

Answer 2

ANSWER:

16x²+4y²+9z²-16xy-12yz+24xz

= (4x)²+(-2y)²+(3z)²+2{4x(-2y)+(-2y)

(3z)+(3z)(-4x)

=(4x-2y+3z)²

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