1. Objective 123 Multiplying binomials by trinomials ©2002 by R. Villar All Rights Reserved

2. Multiplying binomials by trinomials To multiply a binomial by a trinomial, we cannot use the FOIL method…it only works for binomials by binomials… Instead, we must distribute... Example: Multiply (x + 4)(x 2 + 4x – 2) Distribute each term of the binomial by the trinomial… (x + 4)(x 2 + 4x – 2) x(x 2 + 4x – 2) + 4(x 2 + 4x – 2) x 3 + 4x 2 – 2x + 4x 2 + 16x – 8 Now, collect like terms... x 3 + 8x 2 + 14x – 8

3. Example: Multiply (2x – 3)(3x 2 – x + 1) Distribute each term of the binomial by the trinomial… (2x – 3)(3x 2 – x + 1) 2x(3x 2 – x + 1) – 3(3x 2 – x + 1) 6x 3 – 2x 2 + 2x – 9x 2 + 3x – 3 Now, collect like terms... 6x 3 – 11x 2 + 5x – 3

4. You can also multiply binomials by trinomials vertically... Example: Multiply 2x 2 – x + 5 x – 3 Multiply as if this was a 2 digit multiplication problem... First, multiply the “one’s place (the –3 in this problem)... –6x 2 + 3x – 15 Then, multiply the “ten’s place (the x in this problem)... 2x 3 – x 2 + 5x Now, add like terms (notice that like term are lined up)... 2x 3 – 7x 2 + 8x – 15