Transcript Lesson 6-2
Lesson 8-6 Multiplying Polynomials by a Monomial Click the mouse button or press the Space Bar to display the answers. Objectives • Find the product of a monomial and a polynomial • Solve equation involving polynomials Vocabulary • none new – sorry no definitions! Check back tomorrow for some!! ^-^ Multiplying Polynomials • Use the Distributive Property of Equality! • Example: 6x(2x2 + 3xy – 5y3 + 4) = 6x(2x2) + 6x(3xy) – 6x(5y3) + 6x(4) = 12x3 + 18x2y – 30xy3 + 24x Example 1 Find 6y(4y2 – 9y – 7) Method 1 Horizontal Distributive Property Multiply. Method 2 Vertical Distributive Property Multiply. Answer: Example 2 Simplify 3(2t2 – 4t – 15) + 6t(5t + 2) Distributive Property Product of Powers Commutative and Associative Properties Combine like terms. Answer: Example 3 Entertainment Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each and regular rides are an additional $2. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. Find an expression for how much money Sarita spent at the park. Words The total cost is the sum of the admission, super ride costs, and regular ride costs. Variables If the number of super rides, then is the number of regular rides. Let M be the amount of money Sarita spent at the park. Example 3 cont Equation Amount super $3 per regular $2 per of money equals admission plus rides times ride plus rides times ride. M 10 s 3 2 Distributive Property Simplify Simplify. Answer: An expression for the amount of money Sarita spent in the park is , where s is the number of super rides she rode. Example 3 cont Evaluate the expression to find the cost if Sarita rode 9 super rides. Add. Answer: Sarita spent $49. Example 4 Solve b(12 + b) – 7 = 2b + b(-4 + b) Original equation Distributive Property Combine like terms. Subtract from each side. Add 7 to each side. Add 2b to each side. Divide each side by 14. Answer: Summary & Homework • Summary: – The Distributive Property can be used to multiply a polynomial by a monomial • Homework: – pg. 446 16-48 even