The FOIL method illustrates a basic principle of simplifying polynomials: Multiply each term in the first group by each term in the second group. In polynomials with two groups of two terms each, use FOIL (First, Outer, Inner, Last). Multiply the first terms in each group, then the outer terms, the inner terms, then the last term in each group, and add the resulting terms.
Like terms share the same variable with the same exponent. They may or may not have the same coefficient. In polynomials involving multiple variables, like terms have exactly the same variables with the same combination of exponents, such as 2ab^3 and 5ab^3. A polynomial is not fully simplified until there is only one of each kind of term. To combine like terms, add the coefficients and keep the same variable and exponent. For example, 2x^2 + 3x^2 = 5x^2.
When a polynomial has more than two terms in one or more of the sets of parentheses, the principle stays the same. Multiply each term in the first group with each term in the second group, then combine like terms. The number of resulting terms (before like terms are combined) should equal the number of terms in the first group times the number of terms in the second group.
Suppose you're asked to simplify (x + 3)(x - 2). So apply the FOIL method:
First: x * x = x^2
Outer: x * -2 = -2x
Inner: 3 * x = 3x
Last: 3 * -2 = -6
Your result is (x + 3)(x - 2) = x^2 - 2x + 3x - 6. Now find the like terms. The middle terms, -2x and 3x, are like terms because they have the same variable (x) with the same exponent. The first term, x^2, has a different exponent, so it is not a like term. Next, combine like terms : -2x + 3x = x. Concluding the example, x^2 - 2x + 3x - 6 = x^2 + x - 6.