When multiplying two expressions, we can distribute all factors into each term of the other expression. With simple algebraic expression, this typically involves a coefficient and a single variable, as in the example below:
We can also use the distribution property with examples involving other variables or exponents:
In the previous examples, we multiplied a monomial (single term expression) by a binomial (two term expression). When multiplying two binomials together, we use a special case of the distributive rule, commonly referred to as FOIL. FOIL stands for First, Outside, Inside, Last, and describes how to distribute all terms in binomial multiplication. This is shown in the example below:
Multiplying Three Binomials
How can the distributive and FOIL processes be modified to multiply three binomials? One strategy is to perform the steps in FOIL to two of the binomials, and then distribute the third binomial into the product revealed by FOIL. This is illustrated in the example below:
So far, all that we have done is used FOIL to multiply two of the three binomials. In order to multiply the third binomial, we will distribute each term in 2x – 1 into every term in x2 – 2x + 3. In order to keep things organized, it is helpful to distribute separately, and then add the two new polynomials:
Our final step is two add the the polynomials after distributing 2x and –1. Remember to use coefficients of 0 to keep the vertical alignment between like terms.