Question

Factorise the following :
$m^2+2mn-24n^2$

Answer 1

$m^2+2mn-24n^2$

$\Rightarrow (m^2+2mn+n^2)-n^2-24n^2$

$\Rightarrow (m+n{)}^2-25n^2$

$\Rightarrow (m+n{)}^2-(5n{)}^2$ $(a^2-b^2=(a+b\left)\right(a-b\left)\right)$

$\Rightarrow (m+n+5n)(m+n-5n)$

$\Rightarrow (m+6n)(m-4n)$.