Question

Work out the following division: $96abc(3a-12)(5b-30)÷144(a-4)(b-6)$

Answer 1

Divide $96abc(3a-12)(5b-30)÷144(a-4)(b-6)$.

Cancel out the common factors.

$\begin{array}{rcl}96abc(3a-12)(5b-30)÷144(a-4)(b-6)& =& \frac{96abc(3a-12)(5b-30)}{144(a-4)(b-6)}\\ & =& \frac{96abc\left(3(a-4)\right)\left(5(b-6)\right)}{144(a-4)(b-6)}\\ & =& \frac{96abc\times 3\times 5\times \left(a-4\right)(b-6)}{144(a-4)(b-6)}\\ & =& \frac{96abc\times 3\times 5}{144}\\ & =& 10abc\end{array}$

Thus, the quotient for given division of polynomial is $10abc$.