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

2 Answers
Jun 3, 2015

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

Jun 3, 2015

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