Section 2'2 Simplifying Expressions

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Section 2.2 Simplifying Expressions Similar
(Like) Terms have the same variable(s) and
exponents. The number in front of the variable
(coefficient) can differ.
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Steps for Adding and Subtracting Polynomials
1. Rewrite expression without parenthesis If
necessary, make sure to distribute distribute
negative through parentheses 2. Identify like
___________________
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Steps for Adding and Subtracting Polynomials
3. Add/subtract the ________________ (number in
front of variable) copy the variable
Variables always stay the same in addition
and subtraction 4. Write each answer with the
variables in alphabetical order and any constant
term last.
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• Simplify (Combine Like terms)
• 3x 5x 2. 4x x
• 3. 9y 11y 4. 2y y

5. 10t 18t 6. 5x 8x 3x
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Simplify (Combine Like terms)
7. x2 3x 2x2 4x 8. x3 x2 2x2 x3
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Simplify (Combine Like terms)
9. 5x2 2x 7y 2x2 3x 4y 10. 3x3y2
2x2y3 5x3y2 2x2y3 4xy3
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Review of Associative Property of
Multiplication (a b) c a (b c)
Simplify by using the associative property of
multiplication. 11. 8(2x) 12. 7(3x2)
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Review of Distributive Property a(b c) ab
ac
Note If there is no number (coefficient) in
front of the variable, the number is 1.
Therefore, x 1x
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Use the distributive property to simplify each
expression. 13. 2(3x 4) 14. 4(5 2x)
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15. 3(x 1) 16. 6(2x 4y)
17. 2(3 2x) 18. 5(5a 3b 2c)
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Simplify each expression. 19. 8 2(x 3)
20. 3 4(2 3x)
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Simplify each expression. 21. 5(2x 1) 6
22. 2(3x2 4) 3x2
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23. y 2(3 2y) 6 25. 7y 3(5x 4y)
10x
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Homework
Pg. 103 1 49 eoo, 12, 18, 24, 30, 32, 38, 46,
51 75 odd, 56, 58, 64, 70, 74, 76, 83 88 all
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Section 2.3 Solving Equations Using Addition A
solution for an equation is a number that makes
the equation a true statement.
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Check to see if the number is a solution to the
equation 1. Determine if x -6 is a solution
to 4x 5 2x 1
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Check to see if the number is a solution to the
equation
2. Determine if x -5 is a solution to x 8
3x 2
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Addition Property of Equality If A B Then A
C B C A, B, C are algebraic expressions
? Adding (or subtracting) the same number to
both sides of an equation never changes the
solution to the equation.
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Solve the following equations using the addition
property of equality 3. x 5 10 4. x 5
10 5. x 5 10
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Solve the following equations using the addition
property of equality 6. x 5 10 7. 15
2 x 8. 15 x 2
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Simplify first then solve the following equations
using the addition property of equality 9. x
8 2 7 1
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Simplify first then solve the following equations
using the addition property of equality 10.
5x 6 4x 4
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Simplify first then solve the following equations
using the addition property of equality
11. 7x 6 6x 3 1
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Simplify first then solve the following equations
using the addition property of equality 12.
3 6 9 7x 5 6x
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Simplify first then solve the following equations
using the addition property of equality 13.
6x 7(x 1) 20 5
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Simplify first then solve the following equations
using the addition property of equality
14. 4 2(x 3) 3x 2 5 1
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Homework
Pg. 113 11, 13, 21, 29 57 odd, 34, 38, 40,
44, 52, 58, 63, 67, 68, 69, 70