Question

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

Answer 1

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 `(2x-3)(5+x^2-3x)`

First, we multiply `2x` by all the `(5+x^2-3x)` factor, and then we do the same for `-3`.

So,
`2x(5+x^2-2x)=10x+2x^3-4x^2)`
`-3(5+x^2-2x)=-15-3x^2+6x`

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

Final answer: `2x^3-7x^2+16x-15`