1. Multiplying Polynomials Module VII, Lesson 3 Online Algebra VHS@PWCS

2. Multiplying Polynomials Recall that to multiply a polynomial by a monomial, we used the distributive property. 3x(2x 2 – 7x + 8) 3x(2x 2 ) – 3x(7x) + 3x(8) 6x 3 – 21x 2 + 24x

3. Multiplying Binomials We apply the distributive property when multiplying binomials using a method called FOIL. FOIL stands for: First – Multiply the first terms Outside – Multiply the outside terms Inside – Multiply the inside terms Last – Multiply the last terms ( + )( + ) x(x)+ 7x+ 5x+ 5(7) x 2 +12x + 35

4. Try these using FOIL (x – 8)(x + 7) First x(x) = x 2 Outside 7x Inside -8x Last -8(7) = -56 Put it all together: x 2 + 7x + -8x + -56 x 2 - x - 56 (2x + 9)(3x – 10) First 2x(3x) = 6x 2 Outside 2x(-10) = -20x Inside 9(3x) = 27x Last 9(-10) = -56 Put it all together: 6x 2 + -20x + 27x + -56 6x 2 + 7x - 56

5. Multiplying Polynomials by Polynomials (3x 2 – 2x + 3)(2x + 7) Like with adding and subtracting polynomials it is easier to multiply setting these on top of each other. In this manner we can multiply as we have always done. 1. Multiply everything in the first factor by 7 2. Multiply everything in the first factor by 2x, using a placeholder. 3. Add the products. 6x 3 + 17x 2 – 8x + 21

6. Try these on your own. (x – 3)(2x 2 + 3x + 3) 2x 2 + 3x + 3 x – 3 -6x 2 – 9x – 9 2x 3 + 3x 2 + 3x 2x 3 - 3x 2 - 6x - 9 (2t 2 – 6t + 3)(2t – 5) 2t 2 – 6t + 3 2t – 5 -10t 2 + 30t – 15 4t 3 – 12t 2 + 6t 4t 3 – 22t 2 + 36t - 15

7. Wrap up  We use FOIL to multiply 2 binomials  First  Outside  Inside  Last  We can set up multiplying polynomials as we have always done and follow those rules.