Question

Factorise the following expression: $p^4-81$

Answer 1

Factorise the given expression:

The given expression is,

$p^4-81={\left(p^2\right)}^2-{\left(3^2\right)}^2$

$=(p^2+3^2)(p^2-3^2)$ $\left[\because a^2-b^2=(a+b)(a-b)\right]$

$=(p^2+9)(p+3)(p-3)$ $\left[\because a^2-b^2=(a+b)(a-b)\right]$

Hence, the factors are $(p+3),(p-3)$ and $(p^2+9).$.