Simplifying Polynomials

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# Simplifying Polynomials - PowerPoint PPT Presentation

Simplifying Polynomials. 13-2. Warm Up. x. 1. 2. 2. Identify the coefficient of each monomial. 1. 3 x 4 2. ab 3. 4. – cb 3 Use the Distributive Property to simplify each expression. 5. 9(6 + 7) 6. 4(10 – 2). 3. 1. –1. 32. 117. Learn to simplify polynomials .

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### Simplifying Polynomials

13-2

Warm Up

x

1

2

2

Identify the coefficient of each monomial.

1.3x42.ab

3.4. –cb3

Use the Distributive Property to simplify each expression.

5. 9(6 + 7) 6. 4(10 – 2)

3

1

–1

32

117

Examples: Identifying Like Terms

3

2

2

3

5x + y + 2 – 6y + 4x

Like terms: 5x3 and 4x3, y2 and –6y2

Like terms: 3a3b2, 2a3b2, and –a3b2

3

2

3

2

2

3

2

3

3a b + 3a b + 2a b – a b

Identify like terms.

Identify like terms.

Identify the like terms in each polynomial.

A. 5x3 + y2 + 2 – 6y2 + 4x3

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

Example: Identifying Like Terms

7p3q2 + 7p2q3 + 7pq2

There are no like terms.

Identify like terms.

Identify the like terms in the polynomial.

C. 7p3q2 + 7p2q3 + 7pq2

Try This

4

2

2

4

4y + y + 2 – 8y + 2y

Like terms: 4y4 and 2y4, y2 and –8y2

7n4r2 + 3a2b3 + 5n4r2 + n4r2

Identify like terms.

Identify like terms.

Identify the like terms in each polynomial.

A. 4y4 + y2 + 2 – 8y2 + 2y4

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

Like terms: 7n4r2, 5n4r2, and n4r2

Try This

There are no like terms.

Identify the like terms.

Identify the like terms in the polynomial.

C. 9m3n2 + 7m2n3 + pq2

9m3n2 + 7m2n3 + pq2

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.

Example: Simplifying Polynomials by Combining Like Terms

4x2 + 2x2– 6x + 7 + 9

2

6x – 6x + 16

Identify like terms.

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

Arrange in descending order.

Simplify.

A. 4x2 + 2x2 + 7 – 6x + 9

4x2 + 2x2 – 6x + 7 + 9

Example: Simplifying Polynomials by Combining Like Terms

3n5m4+ n5m4 –6n3m – 8n3m

3n5m4+ n5m4 –6n3m – 8n3m

4n5m4–14n3m

Arrange in descending order.

Identify like terms.

Combine coefficients:

3 + 1 = 4 and –6 – 8 = – 14.

Simplify.

B. 3n5m4–6n3m + n5m4 – 8n3m

Try This

Identify the like terms.

Combine coefficients: 2 + 5 = 7 and 6 + 9 = 15

Arrange in descending order.

Simplify.

A. 2x3+ 5x3 + 6 – 4x + 9

2x3+ 5x3 – 4x + 6 + 9

2x3+ 5x3 – 4x + 6 + 9

7x3– 4x + 15

Try This

Arrange in descending order.

Identify like terms.

Combine coefficients:

2 + 1 = 3 and –7 + –9 = –16

Simplify.

B. 2n5p4–7n6p + n5p4 – 9n6p

2n5p4+ n5p4 –7n6p – 9n6p

2n5p4+ n5p4 –7n6p – 9n6p

3n5p4–16n6p

2

3

3(x + 5x )

2

3

3 x + 3  5x

2

3

3x + 15x

Distributive Property

Simplify.

A. 3(x3 + 5x2)

–4(3m3n + 7m2n) + m2n

–4  3m3n – 4  7m2n + m2n

–12m3n – 28m2n + m2n

–12m3n – 27m2n

Distributive Property

Combine like terms.

Simplify.

B. –4(3m3n + 7m2n) + m2n

Try This

2(x3+ 5x2)

2  x3 + 2  5x2

2x3 + 10x2

Distributive Property

Simplify.

A. 2(x3 + 5x2)

Try This

–2(6m3p + 8m2p) + m2p

–2  6m3p – 2  8m2p + m2p

–12m3p – 16m2p + m2p

–12m3p – 15m2p

Distributive Property

Combine like terms.

Simplify.

B. –2(6m3p + 8m2p) + m2p

2

2

2(r + rh) =

2r + 2rh

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.

Try This

2

2

3a(b + c) =

3ab + 3ac

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

Lesson Quiz

2

2

2x and 5x , z and –3z

2ab2 and –5ab2, 4a2b and a2b

15x2 + 10

6k2 + 8k + 8

12mn2 + 9n

3h3–5h2 + 8h – 9

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