Question

How do you factor completely: $16{\mathrm{x}}^2+40\mathrm{x}+25$?

Answer 1

Factorize the given expression:

Given polynomial is $16{\mathrm{x}}^2+40\mathrm{x}+25$

Here $16{\mathrm{x}}^2+40\mathrm{x}+25={\left(4\mathrm{x}\right)}^2+2\times 4\mathrm{x}\times 5+5^2$

$\Rightarrow$ $16{\mathrm{x}}^2+40\mathrm{x}+25={\left(4\mathrm{x}+5\right)}^2$ ; $\left[\because {\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2={\left(\mathrm{a}+\mathrm{b}\right)}^2\right]$

Hence, factorized form of $16{\mathrm{x}}^2+40\mathrm{x}+25$ is ${\left(4\mathrm{x}+5\right)}^2$.