Question

Factorise: $(x+5{)}^2-4(x+5)$

Answer 1

Given $(x+5{)}^2-4(x+5)$
Use the formula of $(a+b{)}^2=a^2+2ab+b^2$ to expand $(x+5{)}^2=x^2+5^2+2(x\left)\right(5)$
Thus, given expression is
$(x+5{)}^2-4(x+5)=x^2+5^2+2(x\left)\right(5)-4(x+5)$
$=x^2+10x+25-4x-20$
$=x^2+6x+5$
$=x^2+5x+1x+5$
$=x(x+5)+1(x+5)$
$=(x+5)(x+1)$
Therefore, the factorised form of the given expression is $(x+5{)}^2-4(x+5)=(x+5\left)\right(x+1)$