# How do you find the product (5 + x^2 - 2x) (2x - 3)?

May 18, 2015

You just multiply first one element by all the elements in the other factor, then proceed the same way.

For example, let's just rearrange it as $\left(2 x - 3\right) \left(5 + {x}^{2} - 3 x\right)$

First, we multiply $2 x$ by all the $\left(5 + {x}^{2} - 3 x\right)$ factor, and then we do the same for $- 3$.

So,
2x(5+x^2-2x)=10x+2x^3-4x^2)
$- 3 \left(5 + {x}^{2} - 2 x\right) = - 15 - 3 {x}^{2} + 6 x$

Now, we just sum these results up, combining those elements with the same exponent in the variable $x$.

Final answer: $2 {x}^{3} - 7 {x}^{2} + 16 x - 15$