# How do you multiply (10w-8)/(w+2)*(3w^2-w-14)/(25w^2-16)?

Apr 1, 2018

$\frac{6 w - 14}{5 w + 4}$

#### Explanation:

$25 {w}^{2} - 16$ should be screaming "the difference of two squares" to you. $\left(5 w - 4\right) \left(5 w + 4\right)$
So look to factorise the other terms:

$\frac{2 \left(5 w - 4\right)}{w + 2}$$\times$ $\frac{\left(w + 2\right) \left(3 w - 7\right)}{\left(5 w - 4\right) \left(5 w + 4\right)}$

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$\frac{2}{1}$$\times$$\frac{3 w - 7}{5 w + 4}$

$\implies$ $\frac{6 w - 14}{5 w + 4}$