Course 3

14-2 Simplifying Polynomials14-2 Simplifying Polynomials

Course 3

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Course 3

14-2 Simplifying Polynomials

Warm UpIdentify the coefficient of each monomial.

1. 3x4 2. ab

3. 4. –cb3

Use the Distributive Property to simplify each expression.

5. 9(6 + 7) 6. 4(10 – 2)

3 1

–1x2

12

117 32

Course 3

14-2 Simplifying Polynomials

Problem of the DayWarren 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 3

14-2 Simplifying Polynomials

Learn to simplify polynomials.

Course 3

14-2 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.

4a3b2 + 3a2b3 – 2a3b2

Like terms

Not like terms

The variables have the same powers.

The variables have different powers.

Course 3

14-2 Simplifying Polynomials

Additional Example 1: Identifying Like TermsIdentify the like terms in each polynomial.A. 5x3 + y2 + 2 – 6y2 + 4x3

B. 3a3b2 + 3a2b3 + 2a3b2 - a3b2

Identify like terms. 5x + y + 2 – 6y + 4x3 2 2 3

Like terms: 5x3 and 4x3, y2 and –6y2

3a b + 3a b + 2a b – a b3 2 2 33 3 2 2 Identify like terms.

Like terms: 3a3b2, 2a3b2, and –a3b2

Course 3

14-2 Simplifying Polynomials

Additional Example 1: Identifying Like TermsIdentify the like terms in the polynomial.C. 7p3q2 + 7p2q3 + 7pq2

Identify like terms. There are no like terms.

7p3q2 + 7p2q3 + 7pq2

Course 3

14-2 Simplifying Polynomials Check It Out: Example 1

Identify the like terms in each polynomial.A. 4y4 + y2 + 2 – 8y2 + 2y4

B. 7n4r2 + 3a2b3 + 5n4r2 + n4r2

Identify like terms. 4y + y + 2 – 8y + 2y4 2 2 4

Like terms: 4y4 and 2y4, y2 and –8y2

7n4r2 + 3a2b3 + 5n4r2 + n4r2 Identify like terms.

Like terms: 7n4r2, 5n4r2, and n4r2

Course 3

14-2 Simplifying Polynomials Check It Out: Example 1

Identify the like terms in the polynomial.C. 9m3n2 + 7m2n3 + pq2

Identify the like terms. There are no like terms.

9m3n2 + 7m2n3 + pq2

Course 3

14-2 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 3

14-2 Simplifying Polynomials Additional Example 2A: Simplifying Polynomials by

Combining Like TermsSimplify.4x2 + 2x2 + 7 – 6x + 9

Identify like terms. 4x2 + 2x2– 6x + 7 + 9

26x – 6x + 16 Combine coefficients: 4 + 2 = 6 and 7 + 9 = 16

Arrange in descending order.

4x2 + 2x2 – 6x + 7 + 9

Course 3

14-2 Simplifying Polynomials Additional Example 2B: Simplifying Polynomials by

Combining Like TermsSimplify.3n5m4 – 6n3m + n5m4 – 8n3m

Arrange in descending order.

Identify like terms.

3n5m4 + n5m4 – 6n3m – 8n3m

Combine coefficients: 3 + 1 = 4 and –6 – 8 = –14.

3n5m4 + n5m4 – 6n3m – 8n3m

4n5m4 – 14n3m

Course 3

14-2 Simplifying Polynomials Check It Out: Example 2A

Simplify.

2x3+ 5x3 + 6 – 4x + 9

Identify the like terms. Combine coefficients: 2 + 5 = 7 and 6 + 9 = 15

Arrange in descending order.

2x3+ 5x3 – 4x + 6 + 92x3+ 5x3 – 4x + 6 + 97x3 – 4x + 15

Course 3

14-2 Simplifying Polynomials Check It Out: Example 2B

Simplify.2n5p4 – 7n6p + n5p4 – 9n6p

Arrange in descending order. Identify like terms.

Combine coefficients: 2 + 1 = 3 and –7 + –9 = –16

2n5p4 + n5p4 – 7n6p – 9n6p

2n5p4 + n5p4 – 7n6p – 9n6p

3n5p4 – 16n6p

Course 3

14-2 Simplifying Polynomials

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

Course 3

14-2 Simplifying Polynomials Additional Example 3A: Simplifying Polynomials by

Using the Distributive PropertySimplify.3(x3 + 5x2)

23(x + 5x )3 Distributive Property

3 x3 + 3 5x2

23x + 15x 3

Course 3

14-2 Simplifying Polynomials Additional Example 3B: Simplifying Polynomials by

Using the Distributive PropertySimplify.–4(3m3n + 7m2n) + m2n

Distributive Property –4(3m3n + 7m2n) + m2n

–4 3m3n – 4 7m2n + m2n

–12m3n – 28m2n + m2n

–12m3n – 27m2n Combine like terms.

Course 3

14-2 Simplifying Polynomials Check It Out: Example 3A

Simplify.2(x3 + 5x2)

2(x3+ 5x2) Distributive Property 2 x3 + 2 5x2

2x3 + 10x2

Course 3

14-2 Simplifying PolynomialsCheck It Out: Example 3B

Simplify.–2(6m3p + 8m2p) + m2p

Distributive Property –2(6m3p + 8m2p) + m2p

–2 6m3p – 2 8m2p + m2p

–12m3p – 16m2p + m2p

–12m3p – 15m2p Combine like terms.

Course 3

14-2 Simplifying Polynomials Additional Example 4: Business Application

The surface area of a right cylinder can be found by using the expression 2(r2 + rh), where r is the radius and h is the height. Use the Distributive Property to write an equivalent expression.

2(r2 + rh) = 2r2 + 2 rh

Pre-Algebra

14-2 Simplifying Polynomials

Course 3

14-2 Simplifying Polynomials Check It Out: Example 4

Use the Distributive Property to write an equivalent expression for 3a(b2+ c).

3a(b + c) = 2 3ab + 3ac2

Pre-Algebra

14-2 Simplifying Polynomials

Course 3

14-2 Simplifying PolynomialsLesson Quiz

Identify the like terms in each polynomial.

1. 2x2 – 3z + 5x2 + z + 8z2

2. 2ab2 + 4a2b – 5ab2 – 4 + a2b

Simplify.

3. 5(3x2 + 2)

4. –2k2 + 10 + 8k2 + 8k – 2

5. 3(2mn2 + 3n) + 6mn2

Insert Lesson Title Here

2x and 5x , z and –3z2 2

2ab2 and –5ab2, 4a2b and a2b

15x2 + 10

6k2 + 8k + 8

12mn2 + 9n

Pre-Algebra

14-2 Simplifying Polynomials