Course Simplifying Polynomials 14-2 Simplifying Polynomials Course 3 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Course Simplifying Polynomials Warm Up Identify the coefficient of each monomial. 1. 3x 4 2. ab –cb 3 Use the Distributive Property to simplify each expression. 5. 9(6 + 7)6. 4(10 – 2) 3 1 –1 x

Course Simplifying Polynomials Problem of the Day Warren drank 3.5 gallons of water in one week. Find the average number of ounces of water Warren drank each day that week. 64 oz

Course Simplifying Polynomials Learn to simplify polynomials.

Course Simplifying Polynomials You can simplify a polynomial by adding or subtracting like terms. Remember that like terms have the same variables raised to the same powers. 4a 3 b 2 + 3a 2 b 3 – 2a 3 b 2 Like terms Not like terms The variables have the same powers. The variables have different powers.

Course Simplifying Polynomials Additional Example 1: Identifying Like Terms Identify the like terms in each polynomial. A. 5x 3 + y – 6y 2 + 4x 3 B. 3a 3 b 2 + 3a 2 b 3 + 2a 3 b 2 - a 3 b 2 Identify like terms. 5x + y + 2 – 6y + 4x Like terms: 5x 3 and 4x 3, y 2 and –6y 2 3a b + 3a b + 2a b – a b Identify like terms. Like terms: 3a 3 b 2, 2a 3 b 2, and –a 3 b 2

Course Simplifying Polynomials Additional Example 1: Identifying Like Terms Identify the like terms in the polynomial. C. 7p 3 q 2 + 7p 2 q 3 + 7pq 2 Identify like terms. There are no like terms. 7p 3 q 2 + 7p 2 q 3 + 7pq 2

Course Simplifying Polynomials Check It Out: Example 1 Identify the like terms in each polynomial. A. 4y 4 + y – 8y 2 + 2y 4 B. 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2 Identify like terms. 4y + y + 2 – 8y + 2y Like terms: 4y 4 and 2y 4, y 2 and –8y 2 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2 Identify like terms. Like terms: 7n 4 r 2, 5n 4 r 2, and n 4 r 2

Course Simplifying Polynomials Check It Out: Example 1 Identify the like terms in the polynomial. C. 9m 3 n 2 + 7m 2 n 3 + pq 2 Identify the like terms. There are no like terms. 9m 3 n 2 + 7m 2 n 3 + pq 2

Course Simplifying Polynomials To simplify a polynomial, combine like terms. It may be easier to arrange the terms in descending order (highest degree to lowest degree) before combining like terms.

Course Simplifying Polynomials Additional Example 2A: Simplifying Polynomials by Combining Like Terms Simplify. 4x 2 + 2x – 6x + 9 Identify like terms. 4x 2 + 2x 2 – 6x x – 6x + 16 Combine coefficients: = 6 and = 16 Arrange in descending order. 4x 2 + 2x 2 – 6x

Course Simplifying Polynomials Additional Example 2B: Simplifying Polynomials by Combining Like Terms Simplify. 3n 5 m 4 – 6n 3 m + n 5 m 4 – 8n 3 m Arrange in descending order. Identify like terms. 3n 5 m 4 + n 5 m 4 – 6n 3 m – 8n 3 m Combine coefficients: = 4 and –6 – 8 = –14. 3n 5 m 4 + n 5 m 4 – 6n 3 m – 8n 3 m 4n 5 m 4 – 14n 3 m

Course Simplifying Polynomials Check It Out: Example 2A Simplify. 2x 3 + 5x – 4x + 9 Identify the like terms.Combine coefficients: = 7 and = 15 Arrange in descending order. 2x 3 + 5x 3 – 4x x 3 – 4x + 15

Course Simplifying Polynomials Check It Out: Example 2B Simplify. 2n 5 p 4 – 7n 6 p + n 5 p 4 – 9n 6 p Arrange in descending order. Identify like terms. Combine coefficients: = 3 and –7 + –9 = –16 2n 5 p 4 + n 5 p 4 – 7n 6 p – 9n 6 p 3n 5 p 4 – 16n 6 p

Course Simplifying Polynomials Sometimes you may need to use the Distributive Property to simplify a polynomial.

Course Simplifying Polynomials Additional Example 3A: Simplifying Polynomials by Using the Distributive Property Simplify. 3(x 3 + 5x 2 ) 2 3(x + 5x ) 3 Distributive Property3  x  5x 2 2 3x + 15x 3

Course Simplifying Polynomials Additional Example 3B: Simplifying Polynomials by Using the Distributive Property Simplify. –4(3m 3 n + 7m 2 n) + m 2 n Distributive Property –4(3m 3 n + 7m 2 n) + m 2 n –4  3m 3 n – 4  7m 2 n + m 2 n –12m 3 n – 28m 2 n + m 2 n –12m 3 n – 27m 2 n Combine like terms.

Course Simplifying Polynomials Check It Out: Example 3A Simplify. 2(x 3 + 5x 2 ) Distributive Property 2  x  5x 2 2x x 2

Course Simplifying Polynomials Check It Out: Example 3B Simplify. –2(6m 3 p + 8m 2 p) + m 2 p Distributive Property –2(6m 3 p + 8m 2 p) + m 2 p –2  6m 3 p – 2  8m 2 p + m 2 p –12m 3 p – 16m 2 p + m 2 p –12m 3 p – 15m 2 p Combine like terms.

Course Simplifying Polynomials Additional Example 4: Business Application The surface area of a right cylinder can be found by using the expression 2(r 2 + rh), where r is the radius and h is the height. Use the Distributive Property to write an equivalent expression. 2(r 2 + rh) = 2r 2 + 2 rh Pre-Algebra 14-2 Simplifying Polynomials

Course Simplifying Polynomials Check It Out: Example 4 Use the Distributive Property to write an equivalent expression for 3a(b 2 + c). 3a(b + c) = 2 3ab + 3ac 2 Pre-Algebra 14-2 Simplifying Polynomials

Course Simplifying Polynomials Lesson Quiz Identify the like terms in each polynomial. 1. 2x 2 – 3z + 5x 2 + z + 8z ab 2 + 4a 2 b – 5ab 2 – 4 + a 2 b Simplify. 3. 5(3x 2 + 2) 4. –2k k 2 + 8k – (2mn 2 + 3n) + 6mn 2 Insert Lesson Title Here 2x and 5x, z and –3z 22 2ab 2 and –5ab 2, 4a 2 b and a 2 b 15x k 2 + 8k mn 2 + 9n Pre-Algebra 14-2 Simplifying Polynomials