Question

Factorise:

${\left(x-5\right)}^2-36$

Answer 1

$(x-5{)}^2-36$

$\Rightarrow (x-5{)}^2-6^2$

$\Rightarrow \left[\right(x-5)-6]\left[\right(x-5)+6]$ $[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]$

$\Rightarrow (x-11)(x+1)$

$\therefore (x-5{)}^2-36=(x-11\left)\right(x+1)$.