Question

$\text{Factorise the expression:}5m^2+50m+125$

(3 marks)

Answer 1

$\text{Given expression:}5m^2+50m+125$

$\text{Taking the common factor 5 from}\text{all the terms, we get,}5m^2+50m+125=5(m^2+10m+25)...\left(i\right)$

(0.5 mark)

$\text{Now, consider the expression}{m}^2+10m+25\text{from (i)}$

$\text{Using the identity:}(a+b{)}^2=a^2+2ab+b^2,$

(1 mark)

$\text{The expression}{m}^2+10m+25\text{can be written as,}{m}^2+2m\left(5\right)+5^2$

$\Rightarrow m^2+2m\left(5\right)+5^2=(m+5{)}^2...(ii)$

(0.5 mark)

$\text{From (i) and (ii), we get}5m^2+50m+125=5(m^2+10m+25)=5(m+5{)}^2$

(0.5 mark)

$\text{Hence, the factorised form of the}\text{expression}5m^2+50m+125\text{is}5(m+5{)}^2.$

(0.5 mark)