Splash Screen Unit 8 Quadratic Expressions and Equations EQ: How do you use addition, subtraction, multiplication, and factoring of polynomials in order.

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Presentation transcript:

Splash Screen Unit 8 Quadratic Expressions and Equations EQ: How do you use addition, subtraction, multiplication, and factoring of polynomials in order to simplify rational expressions?

Splash Screen Essential Question: How do you multiply a polynomial by a monomial and solve equations using their products? Lesson 2 Multiplying a Polynomial by a Monomial

Lesson Menu 5 minute check on previous lesson. Do the first 4 problems!

Over Lesson 8–1 5-Minute Check 1 A.2a 2 + 3a + 8b 2 B.2a 2 + 9a + 7b 2 C.8a a + b 2 D.8a 2 – 3a + 8b 2 Find (6a + 7b 2 ) + (2a 2 – 3a + b 2 ).

Over Lesson 8–1 5-Minute Check 2 A.6x 2 + 4x – 3 B.6x 2 + x – 3 C.4x 2 – 4x – 3 D.4x 2 – x + 3 Find (5x 2 – 3) – (x 2 + 4x).

Over Lesson 8–1 5-Minute Check 3 A.3x 2 + 6x – 7 B.3x x – 10 C.3x 2 – 10x – 6 D.9x x – 10 Find (6x 2 + 2x – 9) – (3x 2 – 8x + 2) + (x + 1).

Over Lesson 8–1 5-Minute Check 5 A.8a 4 – 6a 2 – 2a 3 – 23 B.8a 4 – 2a C. 8a 4 – 2a 3 – 6a 2 – 23 D.8a – 2a 3 – 6a 2 Simplify (8a 4 – 3a 2 – 9) – (2a 3 – 14 – 3a 2 ).

Splash Screen Unit 8 Quadratic Expressions and Equations EQ: How do you use addition, subtraction, multiplication, and factoring of polynomials in order to simplify rational expressions?

Splash Screen Essential Question: How do you multiply a polynomial by a monomial and solve equations using their products? Lesson 2 Multiplying a Polynomial by a Monomial

Then/Now You multiplied monomials. Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials. EQ: How do you multiply a polynomial by a monomial and solve equations using their products?

Then/Now

REMEMBER the Distributive Property: a  (b + c) = a  b + a  c EQ: How do How do you multiply a polynomial by a monomial and solve equations using their products?

Example 1 Multiply a Polynomial by a Monomial Horizontal Method A. Find 6y (4y 2 – 9y – 7). 6y (4y 2 – 9y – 7)Original expression = 6y(4y 2 ) – 6y(9y) – 6y(7)Distributive Property = 24y 3 – 54y 2 – 42yMultiply. Answer: 24y 3 – 54y 2 – 42y

Example 1 Multiply a Polynomial by a Monomial Vertical Method Answer: 24y 3 – 54y 2 – 42y 4y 2 – 9y – 7 (×) 6yDistributive Property 24y 3 – 54y 2 – 42yMultiply. A. Find 6y (4y 2 – 9y – 7).

Example 1 A.6x 2 + 9x + 15 B.6x 3 + 9x x C.5x 3 + 6x 2 + 8x D.6x 2 + 3x + 5 B. Find 3x (2x 2 + 3x + 5).

Example 2 Simplify Expressions A. Simplify 3 (2t 2 – 4t – 15) + 6t (5t + 2). 3 (2t 2 – 4t – 15) + 6t (5t + 2) = 3(2t 2 ) – 3(4t) – 3(15) + 6t(5t) + 6t(2)Distributive Property = 6t 2 – 12t – t tMultiply. = (6t t 2 ) + [(–12t) + 12t] – 45Commutative and Associative Properties = 36t 2 – 45Combine like terms. Answer: 36t 2 – 45

Example 2 A.4y 2 + 9y + 1 B.8y 2 + 5y – 6 C.20y 2 + 9y + 6 D.28y y – 10 B. Simplify 5 (4y 2 + 5y – 2) + 2y (4y + 3).

Then/Now C. Simplify 2h (- 7h 2 – 4h). Answer: -14h 3 – 8h 2

Then/Now D. Simplify - 3rt (- 2t 2 + 3r). Answer: 6rt 3 – 9r 2 t

Then/Now E. Simplify 6t (2t - 3) + 5 (2t 2 + 9t – 3). Answer: 22t t - 15

Then/Now F. Simplify - 2 (3m 3 + 5m + 6) + 3m (2m 2 + 3m + 1). Answer: 9m 2 – 7m - 12

Then/Now G. Simplify - 3g (7g - 2) + 3 (g 2 + 2g + 1) – 3g (- 5g + 3). Answer: -3g 2 + 3g + 3

End of the Lesson Assignment: Worksheet #1 to #17 Assignment: Worksheet #1 to #17 Essential Question: How do you multiply a polynomial by a monomial and solve equations using their products?

Example 4 Equations with Polynomials on Both Sides A. Solve b (12 + b) – 7 = 2b + b (– 4 + b). b (12 + b) – 7 = 2b + b (– 4 + b)Original equation 12b + b 2 – 7= 2b – 4b + b 2 Distributive Property b b – 7 = b 2 – 2b Combine like terms. 12b – 7= – 2bSubtract b 2 from each side. 12b = – 2b + 7 Add 7 to each side. Divide each side by b = 7 Add 2b to each side.

Example 4 Equations with Polynomials on Both Sides Check b (12 + b) – 7 = 2b + b (– 4 + b) Original equation Simplify. Multiply. Subtract.

Example 4 B. Solve x (x + 2) + 2x (x – 3) + 7 = 3x (x – 5) – 12. A. B. C. D.

Then/Now C. Solve: 5 (2t – 1) + 3 = 3 (3t + 2). Answer: x = 8 Did you check?

Then/Now D. Solve: 3 (3x + 2) + 5 = 2 (2x -2). Answer: x = -3 Did you check?

Then/Now E. Solve: 4 (8n + 3) - 5 = 2 (6n + 8) + 1. Answer: x = ½ Did you check?

Then/Now F. Solve: 8 (3y + 1) = 4 (y + 3) - 9. Answer: x = -¼ Did you check?

Then/Now G. Solve: w (w - 5) + 8w = w (w + 2) – 4. Answer: x = - 4 Did you check?

End of the Lesson Assignment: Finish the Worksheet #18 to #33 Essential Question: How do you multiply a polynomial by a monomial and solve equations using their products?