Question

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

Answer 1

This is where FOIL is not quite enough - It's meant for multiplying two binomials together, but here the second expression is a trinomial.

Instead you can break the problem into separate terms using the distributive law, multiply out, then recombine the terms...

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

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

`=(2x^3+10x^2-6x)-(3x^2+15x-9)`

`=2x^3+10x^2-6x-3x^2-15x+9`

`=2x^3+(10-3)x^2-(6+15)x+9`

`=2x^3+7x^2-21x+9`

Answer 2

Alternatively, working with each of the powers of `x` from `x^3` down to `x^0` (i.e. the constant term), match the terms in the first and second bracketed expressions which will multiply to give that power of `x` and add them together, thus:

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

`x^3 : 2x xx x^2 = 2x^3`

`x^2 : (2x xx 5x) + (-3 xx x^2) = 10x^2 - 3x^2 = 7x^2`

`x^1 : (2x xx -3) + (-3 xx 5x) = -6x -15x = -21x`

`x^0 : -3 xx -3 = 9`

Added, give `2x^3+7x^2-21x+9`