1. Multiplying Binomials

2. -Distributive Property 2x(x + 3) = 2x(x) + 2x(3) = 2x 2 + 6x Prior Knowledge

3. How do you multiply two binomials? To multiply a binomial and a binomial, we will use our knowledge of the distributive property as shown from the previous slide. Each term of the first binomial will get distributed with the polynomial that follows. The next slide shows how this will work…

4. Let’s see how this works! Example #1: (x + 7)(x + 2) = x(x + 2) + 7(x + 2) = x(x) + x(2) + 7(x) + 7(2) = x 2 + 2x + 7x + 14 = x 2 + 9x + 14

5. Example #2: (x – 3)(x – 2) = x(x – 2) – 3(x – 2) = x(x) + x(-2) + (-3)(x) + (-3)(-2) = x 2 – 2x – 3x + 6 = x 2 – 5x + 6

6. Example #3: (x + 2) 2 = (x + 2)(x + 2) = x(x + 2) + 2(x + 2) = x(x) + x(2) + 2(x) + 2(2) = x 2 + 2x + 2x + 4 = x 2 + 4x + 4

7. Will our answers always turn out to be a trinomial? Example #4: (x – 10)(x + 10) = x(x + 10) – 10(x + 10) = x(x) + x(10) + (-10)(x) + (-10)(10) = x 2 + 10x – 10x – 100 = x 2 – 100

8. You try … Simplify:(x + 4)(x + 5) = x(x + 5) + 4(x + 5) = x(x) + x(5) + 4(x) + 4(5) = x 2 + 5x + 4x + 20 = x 2 + 9x + 20

9. You try … Expand:(x – 8)(x + 2) = x(x + 2) – 8(x + 2) = x(x) + x(2) + (-8)(x) + (-8)(2) = x 2 + 2x – 8x – 16 = x 2 – 6x – 16

10. Last one! Simplify:(x + 9) 2 = (x + 9)(x + 9) = x(x + 9) + 9(x + 9) = x(x) + x(9) + 9(x) + 9(9) = x 2 + 9x + 9x + 81 = x 2 + 18x + 81