Technical Mathematics, Sixth Edition

2.6. Multiplying a Binomial by a Binomial

To multiply any two multinomials, we multiply every term in one multinomial by each term in the other multinomial, and combine like terms. Here we apply this rule to binomials and later use it for multinomials having any number of terms.

Example 64: Here we multiply two binomials.

We can also multiply two multinomials by using the distributive rule.

TI-89 screen for Example 64.

Example 65: Repeating Example 64 using the distributive rule gives

2.6.1. FOIL Rule

One way to keep track of the terms when multiplying binomials is by the FOIL rule. Multiply the First terms, then Outer, Inner, and Last terms. These products can, of course, be done in any order, but we can avoid getting mixed up if we always follow the same FOIL order.

Example 66: Repeating Example 64,

NOTE

The FOIL rule is only for multiplying binomials.

2.6.1.1. Exercise 6 Multiplying a Binomial by a Binomial

Multiply and simplify.

1. (x + y)(x + z) x² + xy + xz + yz

2. (4a − 3)(a + 2) 4a² + 5a − 6

3. (4m + n)(2m² − n) 8m³ + 2m²n − 4mn − n²

4. (y + 2)(y − 2) y² − 4

5. (2x − y)(x + y) 2x²