Question

In the following exercises, multiply.

$\frac{q^2-2q}{q^2+6q-16}·\frac{q^2-64}{q^2-8q}$

Short answer

The required answer is 1.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{q^2-2q}{q^2+6q-16}·\frac{q^2-64}{q^2-8q}$

Step 2. Simplify the expression.

$\frac{q^2-2q}{q^2+6q-16}·\frac{q^2-64}{q^2-8q}$

Factor the numerator and denominator completely,

$\frac{q\left(q-2\right)}{\left(q+8\right)\left(q-2\right)}·\frac{\left(q-8\right)\left(q+8\right)}{q\left(q-8\right)}$

Multiply the numerators and denominators,

$\frac{q\left(q-2\right)\left(q-8\right)\left(q+8\right)}{q\left(q+8\right)\left(q-2\right)\left(q-8\right)}$

Simplify by dividing out common factors,

$1$