Question

factorise 4x2 + y2 + z2 - 4xy - 2yz + 4xz​

Answer 1

(2x-y+z)^2

so, answer to that ques is sent as pic above

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Answer 2

Question :-

Factorise ${4x}^{2}$ + ${y}^{2}$ + ${z}^{2}$ - $4xy$ - $2yz$ + $4xz$.

Answer :-

We have :-

⠀⠀⠀⠀$\bold {4x}^{2}$ + $\bold {y}^{2}$ + $\bold {z}^{2}$ - $\bold{4xy}$ - $\bold{2yz}$ + $\bold{4xz}$.

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

Using identity :-

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

⠀⠀⠀⠀⠀= $\bold {x}^{2}$ + $\bold {y}^{2}$ + $\bold {z}^{2}$ + $\bold{2xy}$ + $\bold{2yz}$ + $\bold{2zx}$

⠀⠀⠀⠀⠀⠀⠀= ${[2x\:+(-y)\:+z]}^{2}$

⠀⠀⠀⠀⠀⠀⠀= ${(2x-y+z)}^{2}$

⠀⠀⠀⠀⠀⠀⠀= $(2x-y+z)(2x-y+z)$