Question

Factorise $25x^2-64y^2$.

Answer 1

We write
$25x^2-64y^2={\left(5x\right)}^2-{\left(8y\right)}^2$
This is in the form $a^2-b^2$ which factorises to $(a-b)(a+b)$. Thus
$25x^2-64y^2={\left(5x\right)}^2-{\left(8y\right)}^2=(5x-8y)(5x+8y)$.