Question

Factorise the expression and divide them as directed: $4yz\left(z^2+6z-16\right)÷2y\left(z+8\right)$.

Answer 1

Step 1: Factorize the expression $4yz\left(z^2+6z-16\right)$.

Split the middle term of the expression as $-2z+8z$and take out the common factors.

$\begin{array}{rcl}& \Rightarrow & 4yz\left(z^2-2z+8z-16\right)=4yz\left(z\left(z-2\right)+8\left(z-2\right)\right)\\ & =& 4yz\left(z+8\right)\left(z-2\right)\end{array}$

Step 2: Divide the expression by $2y\left(z+8\right)$ to get the final answer.

$\Rightarrow \frac{4yz\left(z+8\right)\left(z-2\right)}{2y\left(z+8\right)}=2z\left(z-2\right)$

Hence, the required final answer is $2z\left(z-2\right)$.