Question

Factorise the following by taking out the common factors:
e) $24m^4{n}^6+56m^6{n}^4–72m^2{n}^2$

Answer 1

Given:
$24m^4{n}^6+56m^6{n}^4–72m^2{n}^2$

The common factor is $8m^2{n}^2$ .

Dividing by $8m^2{n}^2$ in the above expression, we get,

$\left\{\frac{24m^4{n}^6}{8m^2{n}^2}\right\}$ + $\left\{\frac{56m^6{n}^4}{8m^2{n}^2}\right\}$ – $\left\{\frac{72m^2{n}^2}{8m^2{n}^2}\right\}$

$=3m^2{n}^4+7m^4{n}^2–9$

$\therefore 24m^4{n}^6+56m^6{n}^4-72m^2{n}^2$
$=8m^2{n}^2(3m^2{n}^4+7m^4{n}^2–9)$.