Question

How do you multiply `(2x^2-5x-1)(x^2+x-3)`?

Answer 1

`(2x^2-5x-1)(x^2+x-3)=2x^4-8x^3-12x^2+14x+3`

Explanation:

`(p)*(x^2+x-3) = (px^2+px-3p)`

Replacing `(p)` with `(2x^2-5x-1)`

`(2x^2-5x-1)(x^2+x-3)`
`color(white)("XXXX")` `=(2x^2-5x-1)x^2 +(2x^2-5x-1)x - 3(2x^2-5x-1)`

`color(white)("XXXX")` `=(2x^4-10x^3-x^2)+(2x^3-5x^2-x)-(6x^2-15x-3)`

`color(white)("XXXX")` `=(2x^4) + (-10x^3+2x^3) + (-x^2-5x^2-6x^2) + (-x+15x) + (3)`

`color(white)("XXXX")` `=2x^4-8x^3-12x^2+14x+3`