Expand the following using suitable identity: $(2x-y+z)^2$.

Given :

The given expression is $(2x-y+z)^2$.

To find :

We have to expand the given expression using the suitable identity.

Solution :

We know that,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

On comparison,

$a=2x, b=-y, c=z$

Therefore,

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

                   $=4x^2+y^2+z^2-4xy-2yz+4xz$.

The expansion of $(2x-y+z)^2$ is   $4x^2+y^2+z^2-4xy-2yz+4xz$.

Tutorialspoint

Updated on: 10-Oct-2022

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