Multiply each pair of terms using the FOIL method. For example, consider the polynomial (2x + 3)(x + 6).
Multiply the first term in each set of parentheses:
2x * x = 2x^2
Multiply the outer terms:
2x * 6 = 12x
Multiply the inner terms:
3 * x = 3x
Multiply the last term in each set of parentheses:
3 * 6 = 18
Add the results of the four FOIL multiplications:
(2x + 3)(x + 6) = 2x^2 + 12x + 3x + 18
Find like terms in the result of the FOIL method. Like terms are terms that share the same variable with the same exponent, such as 12x and 3x in the example. Be careful not to combine terms that have the same variable with different exponents, like 3x and 2x^2.
Combine like terms by adding their coefficients, the numbers attached to the variable. In the example, combine 12x and 3x by adding the numbers and attaching the variable:
12x + 3x = 15x
Put this back into the result of the FOIL method:
2x^2 + 12x + 3x + 18 = 2x^2 + 15x + 18
The middle term is 15x.