Question

Factorize: 25x² + 4y² + 9z² − 20xy − 12yz + 30xz.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ 25x^2+4y^2+9z^2-20xy-12yz+30xz \\ ={\left(5x\right)}^2+{\left(-2y\right)}^2+{\left(3z\right)}^2+2\left(5x\right)(-2y)+2(-2y)\left(3z\right)+2\left(3z\right)\left(5x\right) \\ ={\left[\left(5x\right)+\left(-2y\right)+\left(3z\right)\right]}^2 \\ ={\left(5x-2y+3z\right)}^2 \end{gathered}$$