Question

Factorise: $x^2+10x+25$

Answer 1

The expression $x^2+10x+25$ can be written as,

$=x^2+2\times 5\times x+5^2$...(i)

Comparing (i) with the identity $(a+b{)}^2=a^2+2ab+b^2$, we get
$a^2=x^2\Rightarrow a=x$

$b^2=5^2\Rightarrow b=5$

$\Rightarrow$ $x^2+10x+25$=$x^2+2\left(x\right)\left(5\right)+5^2$ = $(x+5{)}^2$
Therefore, the factors of $x^2+10x+25$​​​​​​​ are $(x+5)$ and $(x+5)$.