Question

Factorise:$49x^2-36$.

Answer 1

Factorise the polynomial

$$\begin{gathered} 49x^2-36 \\ ={\left(7x\right)}^2-{\left(6\right)}^2 \end{gathered}$$

using identity ${\mathit{a}}^{\mathbf{2}}\mathbf{-}{\mathit{b}}^{\mathbf{2}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{+}\mathit{b}\mathbf{)}\mathbf{(}\mathit{a}\mathbf{-}\mathit{b}\mathbf{)}$

$=(7x+6)(7x-6)$

Hence, the factors of $49x^2-36$ are $(7x+6)$ and $(7x-6)$.