Question

Factorise the expression $x^2+10x+25$

Answer 1

The given expression contains three terms and the first and third terms are perfect squares. That is $x^2$ and 25 $\left(5^2\right)$. Also the middle term contains the positive sign. This suggests that it can be written in the form of $a^2+2ab+b^2$, so $x^2+10x+25=(x{)}^2+2(x\left)\right(5)+(5{)}^2$
We can compare it with $a^2+2ab+b^2$ which in turn is equal to the LHS of the identity ie. $(a+b{)}^2$. Here a = x and b = 5
We have $x^2+10x+25=(x+5{)}^2=(x+5\left)\right(x+5)$