How do you multiply (6x-4)(7x^2+x-4)?

Mar 21, 2017

$42 {x}^{3} - 22 {x}^{2} - 28 x + 16$

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This can be done as follows.

$\left(\textcolor{red}{6 x - 4}\right) \left(7 {x}^{2} + x - 4\right)$

$= \textcolor{red}{6 x} \left(7 {x}^{2} + x - 4\right) \textcolor{red}{- 4} \left(7 {x}^{2} + x - 4\right)$

distribute and simplify.

$= 42 {x}^{3} + 6 {x}^{2} - 24 x - 28 {x}^{2} - 4 x + 16$

$= 42 {x}^{3} + \left(6 {x}^{2} - 28 {x}^{2}\right) + \left(- 24 x - 4 x\right) + 16$

$= 42 {x}^{3} - 22 {x}^{2} - 28 x + 16$