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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
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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
