Question

Factorise the following expression: $a^2+8a+16$

Answer 1

Factorise by using identities

Given, $a^2+8a+16$

We know that ${(a+b)}^2=a^2+b^2+2ab$

Now, compare $a^2+8a+16$ with this identity, we get

$$\begin{gathered} =a^2+16+8a \\ ={\left(a\right)}^2+{\left(4\right)}^2+(2\times a\times 4) \\ ={(a+4)}^2 \end{gathered}$$

Therefore, the factorisation of $a^2+8a+16$ will be ${(a+4)}^2$.