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

2. Warm Up
Identify the coefficient of each monomial.
1. 3x ab
–cb3
Use the Distributive Property to simplify each expression.
5. 9(6 + 7) 6. 4(10 – 2) 3 1 x 2 1 2 –1
117 32

3. 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

4. Learn to simplify polynomials.

5. You can simplify a polynomial by adding or subtracting like terms
You can simplify a polynomial by adding or subtracting like terms. Remember that like terms have the same variables raised to the same powers.
Like terms
The variables have the same powers.
4a3b2 + 3a2b3 – 2a3b2
Not like terms
The variables have different powers.

6. Additional Example 1: Identifying Like Terms
Identify the like terms in each polynomial.
A. 5x3 + y – 6y2 + 4x3
B. 3a3b2 + 3a2b3 + 2a3b2 - a3b2
5x + y + 2 – 6y + 4x 3 2
Identify like terms.
Like terms: 5x3 and 4x3, y2 and –6y2
Identify like terms.
3a b + 3a b + 2a b – a b 3 2
Like terms: 3a3b2, 2a3b2, and –a3b2

7. Additional Example 1: Identifying Like Terms
Identify the like terms in the polynomial.
C. 7p3q2 + 7p2q3 + 7pq2
7p3q2 + 7p2q3 + 7pq2
Identify like terms.
There are no like terms.

8. Identify the like terms in each polynomial.
Check It Out: Example 1
Identify the like terms in each polynomial.
A. 4y4 + y – 8y2 + 2y4
B. 7n4r2 + 3a2b3 + 5n4r2 + n4r2
4y + y + 2 – 8y + 2y 4 2
Identify like terms.
Like terms: 4y4 and 2y4, y2 and –8y2
7n4r2 + 3a2b3 + 5n4r2 + n4r2
Identify like terms.
Like terms: 7n4r2, 5n4r2, and n4r2

9. Check It Out: Example 1
Identify the like terms in the polynomial.
C. 9m3n2 + 7m2n3 + pq2
9m3n2 + 7m2n3 + pq2
Identify the like terms.
There are no like terms.

10. To simplify a polynomial, combine like terms
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.

11. Additional Example 2A: Simplifying Polynomials by Combining Like Terms
4x2 + 2x2 + 7 – 6x + 9
Arrange in descending order.
4x2 + 2x2 – 6x
4x2 + 2x2– 6x
Identify like terms.
Combine coefficients: = 6 and = 16 2
6x – 6x + 16

12. Additional Example 2B: Simplifying Polynomials by Combining Like Terms
3n5m4 – 6n3m + n5m4 – 8n3m
Arrange in descending order.
3n5m4 + n5m4 – 6n3m – 8n3m
3n5m4 + n5m4 – 6n3m – 8n3m
Identify like terms.
Combine coefficients:
3 + 1 = 4 and –6 – 8 = –14.
4n5m4 – 14n3m

13. Check It Out: Example 2A
Simplify.
2x3+ 5x3 + 6 – 4x + 9
Arrange in descending order.
2x3+ 5x3 – 4x
Identify the like terms.
2x3+ 5x3 – 4x
Combine coefficients: = 7 and = 15
7x3 – 4x + 15

14. Check It Out: Example 2B
Simplify.
2n5p4 – 7n6p + n5p4 – 9n6p
Arrange in descending order.
2n5p4 + n5p4 – 7n6p – 9n6p
Identify like terms.
2n5p4 + n5p4 – 7n6p – 9n6p
Combine coefficients:
2 + 1 = 3 and –7 + –9 = –16
3n5p4 – 16n6p

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

16. Distributive Property
Additional Example 3A: Simplifying Polynomials by Using the Distributive Property
Simplify.
3(x3 + 5x2) 2
3(x + 5x ) 3
Distributive Property
3  x  5x2 2
3x + 15x 3

17. Additional Example 3B: Simplifying Polynomials by Using the Distributive Property
–4(3m3n + 7m2n) + m2n
–4(3m3n + 7m2n) + m2n
Distributive Property
–4  3m3n – 4  7m2n + m2n
–12m3n – 28m2n + m2n
–12m3n – 27m2n
Combine like terms.

18. Check It Out: Example 3A
Simplify.
2(x3 + 5x2)
2(x3+ 5x2)
Distributive Property
2  x3 + 2  5x2
2x3 + 10x2

19. Check It Out: Example 3B
Simplify.
–2(6m3p + 8m2p) + m2p
–2(6m3p + 8m2p) + m2p
Distributive Property
–2  6m3p – 2  8m2p + m2p
–12m3p – 16m2p + m2p
–12m3p – 15m2p
Combine like terms.

20. Additional Example 4: Business Application
Pre-Algebra
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) =
2r2 + 2 rh

21. Simplifying Polynomials
Pre-Algebra
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 + 3ac 2

22. Simplifying Polynomials Insert Lesson Title Here
Pre-Algebra
14-2
Simplifying Polynomials
Insert Lesson Title Here
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. –2k k2 + 8k – 2
5. 3(2mn2 + 3n) + 6mn2
2x and 5x , z and –3z 2
2ab2 and –5ab2, 4a2b and a2b
15x2 + 10
6k2 + 8k + 8
12mn2 + 9n