Question

Factorise the following expression: $49y^2+84yz+36z^2$

Answer 1

Factorise the given expression by using properties

Given, $49y^2+84yz+36z^2$

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

Now, compare this identity with the given expression, we get

$$\begin{gathered} \Rightarrow 49y^2+84yz+36z^2=a^2+b^2+2ab \\ \Rightarrow {\left(7y\right)}^2+{\left(6z\right)}^2+(2\times 7y\times 6z)={\left(a\right)}^2+{\left(b\right)}^2+(2\times a\times b) \\ \Rightarrow {(7y+6z)}^2={(a+b)}^2 \end{gathered}$$

Hence, the factorisation of $49y^2+84yz+36z^2$ will be ${(7y+6z)}^2$.