1. 8.6 Multiplying a Polynomial by a Monomial
What you’ll learn:
To find the product of a monomial and a polynomial.
To solve equations involving polynomials.

2. Multiplying a polynomial by a monomial.
Distribute (multiply coefficients and add exponents on like-bases)
Combine any like-terms.
Ex: -4x²(5x-3x³+7)
-20x³+12x⁵-28x²
Ex: 7a(-5a²-2a)+11a³-7a²
-35a³-14a²+11a³-7a²
-24a³-21a²

3. Find each product.
x(10x-4x²)
-5ab²(-8a³b⁴-5a⁵+3b²)

4. Simplify
3(2x²-4x-15)+6x(5x+2)
2. -3x²(2x+7)+4x(3x²-x+5)+2(x²-4)

5. Solving equations
Distribute, combine like-terms, solve. Ex: -2(x+1)+x=7-4x -2x-2+x=7-4x -x-2=7-4x 3x=9 x=3 Ex: x(x+2)-3x=x(x-4)+5

6. Homework: p. 446 16-46 even p. 837 lesson 8-1 6-18 even