Key Terms
Standard form
A_n(x^n) + ... + a_2(x^2) + a_1(x) + a_0
Rule
Combine like terms only. Like terms share the same variable raised to the same exponent.
Result
4x^3 + 20x^2 + 4x - 1
Example
(x + 4)(3x - 2y + 5) x(3x - 2y + 5) + 4(3x - 2y + 5) = 3x^2 - 2xy + 5x + 12x - 8y + 20 = 3x^2 - 2xy + 17x - 8y + 20
FOIL stands for
First, Outer, Inner, Last. Applies only when multiplying two binomials.
Sum
6x^2 + 6x - 54x - 54 = 6x^2 - 48x - 54
Why it works
The outer and inner terms from FOIL are equal and opposite, so they cancel. Only the squared terms survive.
Note
5x and 12x are like terms (same variable, same exponent). 3x^2 and -2xy are not like terms and cannot be combined.