Question

$\text{Factorise the expression}48+8m-m^2.$

• A. $(4+m)(12-m)$
• B. $(4-m)(12-m)$
• C. $(4+m)(12+m)$
• D. $(6+m)(8-m)$

Answer 1

The correct option is A $(4+m)(12-m)$

$\text{Given:}$
$48+8m-m^2=-(m^2-8m-48)...\left(i\right)$

Now, comparing the expression $m^2-8m-48$ with the identity $x^2+(a+b)x+ab,\text{we get,}$
$(a+b)=-8andab=-48.$
$So,(-12)+4=-8and(-12)\left(4\right)=-48$

Therefore, from (i)
$48+8m-m^2=-(m^2-8m-48)$
$=-[m^2-12m+4m-48]$
$=-\left[m\right(m-12)+4(m-12\left)\right]$
$=-\left[\right(m+4\left)\right(m-12\left)\right]$
$=(m+4)(12-m)$