Pre-Algebra

13-1 Polynomials

Check 13-1 HW

Pre-Algebra

13-2 Simplifying Polynomials

Pre-Algebra HOMEWORK

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Our Learning Goal

Students will be able to classify, simplify,

add and subtract polynomials.

Pre-Algebra

13-1 Polynomials

Students will be able to classify, simplify, add and subtract polynomials by completing the

following assignments.

•Learn to classify polynomials by degree and by

the number of terms.

•Learn to simplify polynomials.

•Learn to add polynomials.

•Learn to subtract polynomials. …..and that’s all folks!

Pre-Algebra

13-1 Polynomials

Today’s Learning Goal Assignment

Learn to simplify polynomials.

Pre-Algebra

13-2 Simplifying Polynomials

13-2 Simplifying Polynomials

Pre-Algebra

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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

Pre-Algebra

13-2 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

Pre-Algebra

13-2 Simplifying Polynomials

Learn to simplify polynomials.

Pre-Algebra

13-2 Simplifying Polynomials

Additional Example 1A & 1B: Identifying Like Terms

Identify 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

Pre-Algebra

13-2 Simplifying Polynomials

Try This: Example 1A & 1B

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

Pre-Algebra

13-2 Simplifying Polynomials

Additional Example 1C: Identifying Like Terms

Identify the like terms in the polynomial.

C. 7p3q2 + 7p2q3 + 7pq2

Identify like terms.

There are no like terms.

7p3q2 + 7p2q3 + 7pq2

Pre-Algebra

13-2 Simplifying Polynomials

Try This: Example 1C

Identify the like terms in the polynomial.

C. 9m3n2 + 7m2n3 + pq2

Identify the like terms.

There are no like terms.

9m3n2 + 7m2n3 + pq2

Pre-Algebra

13-2 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.

Pre-Algebra

13-2 Simplifying Polynomials

Additional Example 2A: Simplifying Polynomials by Combining Like Terms

Simplify.

A. 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

Pre-Algebra

13-2 Simplifying Polynomials

Arrange in descending order.

4x2 + 2x2 – 6x + 7 + 9

Try This: Example 2A

Simplify.

A. 2x3+ 5x3 + 6 – 4x + 9

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

Pre-Algebra

13-2 Simplifying Polynomials

Arrange in descending order.

2x3+ 5x3 – 4x + 6 + 9

2x3+ 5x3 – 4x + 6 + 9

7x3 – 4x + 15

Additional Example 2B: Simplifying Polynomials by Combining Like Terms

Simplify.

B. 3n5m4 – 6n3m + n5m4 – 8n3mArrange in descending order.

Identify like terms.

3n5m4 + n5m4 – 6n3m – 8n3m

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

Pre-Algebra

13-2 Simplifying Polynomials

3n5m4 + n5m4 – 6n3m – 8n3m

4n5m4 – 14n3m

Try This: Example 2B

Simplify.

B. 2n5p4 – 7n6p + n5p4 – 9n6p

Arrange in descending order.

Identify like terms.

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

Pre-Algebra

13-2 Simplifying Polynomials

2n5p4 + n5p4 – 7n6p – 9n6p

2n5p4 + n5p4 – 7n6p – 9n6p

3n5p4 – 16n6p

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

Pre-Algebra

13-2 Simplifying Polynomials

Additional Example 3A: Simplifying Polynomials by Using the Distributive Property

Simplify.

A. 3(x3 + 5x2)

23(x + 5x )3 Distributive Property

23 x + 3 5x 3

23x + 15x 3

Pre-Algebra

13-2 Simplifying Polynomials

Try This: Example 3A

Simplify.

A. 2(x3 + 5x2)

2(x3+ 5x2) Distributive Property

2 x3 + 2 5x2

2x3 + 10x2

Pre-Algebra

13-2 Simplifying Polynomials

Additional Example 3B: Simplifying Polynomials by Using the Distributive Property

Simplify.

B. –4(3m3n + 7m2n) + m2n

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

–4 3m3n – 4 7m2n + m2n

–12m3n – 28m2n + m2n

–12m3n – 27m2n Combine like terms.

Pre-Algebra

13-2 Simplifying Polynomials

Try This: Example 3B

Simplify.

B. –2(6m3p + 8m2p) + m2p

Pre-Algebra

13-2 Simplifying Polynomials

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

–2 6m3p – 2 8m2p + m2p

–12m3p – 16m2p + m2p

–12m3p – 15m2p Combine like terms.

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(r + rh) = 2 2 r + 2 rh 2

Pre-Algebra

13-2 Simplifying Polynomials

Try This: Example 4

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

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

Pre-Algebra

13-2 Simplifying Polynomials

Lesson 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

6. 4h2 + 3h3 – 7 – 9h2 + 8h – 2

Insert Lesson Title Here

2x and 5x , z and –3z2 2

2ab2 and –5ab2, 4a2b and a2b

15x2 + 10

6k2 + 8k + 8

12mn2 + 9n

3h3 – 5h2 + 8h – 9

Pre-Algebra

13-2 Simplifying Polynomials