1. Multiplying a Polynomial by a Monomial
Lesson 13
Multiplying a Polynomial by a Monomial

2. What we are going to do….
Find the product of a monomial and a polynomial.

3. EXAMPLE 1
r(3r + r2) = 3r2 + r3 = r3 + 3r2

4. EXAMPLE 2:
7ab(b3 + 2ab) = 7ab4 + 14a2b2

5. Example 3
5y(4y2 – 9y – 6) = 20y3 – 54y2 – 30y

6. Example 4
-4x2(3x2 – 7x + 10) = -4x2(3x2) – 4x2(-7x) – 4x2(10) = -12x4 + 28x3 – 40x2

7. Example 5
4(2d2 + 5d) – d(d2 – 5d + 12) = 8d2 + 20d – d3 + 5d2 – 12d = -d3 + 8d2 + 5d2 + 20d – 12d = -d3 + 13d2 + 8d

8. Example 6
3(2t2 – 5t – 15) + 6t(3t + 2) = 6t2 – 15t – t2 + 12t = 6t2 + 18t2 – 15t + 12t – 45 = -24t2 - 3t – 45

9. YOUR TURN….
8x2y(3x + 2y2 – 4) = 24x3y + 16x2y3 – 32x2y

10. -2a3b(2b + 5ab – b2 + a3) = -4a3b2 – 10a4b2 + 2a3b3 – 2a6b

11. d(-2d + 6) + 15d = -2d2 + 6d + 15d = -2d2 + 21d

12. 10(4m3 – 3m + 2) – 2m(-3m2 – 7m + 1) = 40m3 – 30m m3 + 14m2 – 2m = 40m3 + 6m3 + 14m2 – 30m – 2m + 20 = 46m3 + 14m2 – 32m + 20

13. -3c2(2c + 7) + 4c(3c2 – c + 5) + 2(c2 – 4) = -6c3 – 21c2 + 12c3 – 4c2 + 20c + 2c2 – 8 = -6c3 + 12c3 – 21c2 – 4c2 + 2c2 + 20c – 8 = 6c3 – 23c2 + 20c – 8