1. Preview
Warm Up
California Standards
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
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3. California
Standards
Preview of Algebra Preparation for Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
Also covered: AF1.3

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

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

6. 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.

7. Check It Out! Example 1
Identify the like terms in each polynomial.
A. 4y4 + y2 + 2 – 8y2 + 2y4
B. 7n4r2 + 3n2r3 + 5n4r2 + n4r2

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

9. To simplify a polynomial, identify like terms
To simplify a polynomial, identify like terms. First arrange the terms from highest degree to lowest degree using the Commutative Property.

10. Additional Example 2: Simplifying Polynomials by Combining Like Terms
A. 4x2 + 2x2 + 7 – 6x + 9

11. When you rearrange terms, move the operation in front of each with that term.
Helpful Hint

12. Additional Example 2: Simplifying Polynomials by Combining Like Terms
B. 3n5m4 – 6n3m + n5m4 – 8n3m

13. Check It Out! Example 2
Simplify.
A. 2x3+ 5x3 + 6 – 4x + 9

14. Check It Out! Example 2
Simplify.
B. 2n5p4 – 7n6p + n5p4 – 9n6p

15. 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
2x2 and 5x2, z and –3z
2ab2 and –5ab2, 4a2b and a2b
15x2 + 10
6k2 + 8k + 8
12mn2 + 9n

16. You may need to use the Distributive Property to simplify a polynomial.

17. Additional Example 3: Simplifying Polynomials by Using the Distributive Property
A. 3(x3 + 5x2)
3(x3 + 5x2)
Distributive Property
3(x3) + 3(5x2)
3x3 + 15x2
No like terms

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

19. Check It Out! Example 3
Simplify.
A. 2(x3 + 5x2)
2(x3+ 5x2)
Distributive Property
2(x3) + 2(5x2)
2x3 + 10x2
No like terms

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

21. 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

22. Check It Out! Example 4
Use the Distributive Property to write an equivalent expression for 3a(b2+ c).
3a(b2 + c) =
3ab2 + 3ac