Question

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

Answer 1

Factorizing the given expression:

The given expression is $4x^2+y^2+z^2-4xy-2yz+4xz$.

Use identity $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$ to expand the expression.

So, expression can be rewritten as:

$4x^2+y^2+z^2-4xy-2yz+4xz={\left(2x\right)}^2+{\left(-y\right)}^2+{\left(z\right)}^2+2\left(2x\right)\left(-y\right)+2\left(-y\right)\left(z\right)+2\left(2x\right)\left(z\right)$

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

So,$4x^2+y^2+z^2-4xy-2yz+4xz$ $={\left[2x+\left(-y\right)+\left(z\right)\right]}^2[\mathrm{Using}\mathrm{identity}]$

Thus, the expression, $4x^2+y^2+z^2-4xy-2yz+4xz={\left(2x-y+z\right)}^2$.