Multiplying Binomials

1. Multiplying Binomials When you multiply 2 things by two things, how many things do you think you will get? 4 One way to remember how to multiply a binomial by a binomial is the FOIL method. FOIL stands for First, Outside, Inside, Last. For example, (a + b)(c + d). First represents the first term in each binomial (a and c). This is one of the four multiplications. ac Outside represents the outer terms in each binomial (a and d). This is the second of the four multiplications. ad Inside represents the inner terms in each binomial (b and c). This is the third of the four multiplications. bc Last represents the last terms in each binomial (b and d). This is the fourth of the four multiplications. bd The product is ac + ad + bc + bd

2. First Outside Inside Last (2y – 3)(y + 2) = (2y)(y) (2y)(2) (-3)(y) + (-3)(2) + + = 2y2 4y 3y 6 + – – = 2y2 1y 6 + – Multiplying Binomials Simplify (2y – 3)(y + 2). Combine like terms if there are any. The product is 2y2 + y – 6.

3. First Outside Inside Last (4x + 2)(3x – 6) = (4x)(3x) (4x)(–6) (2)(3x) + (2)(–6) + + = 12x2 24x 6x 12 – + – = 12x2 18x 12 – – Multiplying Binomials Simplify (4x + 2)(3x – 6). Combine like terms if there are any. The product is 12x2 – 18x – 12.

4. Multiplying Binomials Simplify (5x – 6)(-2x– 7). Another way to multiply binomials is the box method 2) Place one binomial across the top 1) Draw a box with 4 boxes inside. 3) Place the other binomial down the left side 4) Multiply the matching parts of the box 5x – 6 -2x – 7 -10x2 12x -10x2 + 12x – 35x + 42 Combine like terms if there are any. -35x 42 -10x2 – 23x + 42