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Combine Like Terms
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Combine Like TermsCombine Like TermsCombine Like TermsCombine Like TermsI can simplify expressions with I can simplify expressions with
several variables by combining like several variables by combining like terms.terms.
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VocabularyVocabulary
ConstantConstantA number with nothing else A number with nothing else
attached to it. attached to it.
Examples: 1, 2, 47, 925Examples: 1, 2, 47, 925
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VocabularyVocabulary
VariableVariable
A letter that represents an unknown A letter that represents an unknown number. number.
Examples: a, b, x, y Examples: a, b, x, y
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VocabularyVocabulary
CoefficientCoefficient
The number in front of the variable. The number in front of the variable.
Examples: 3x 3 is the coefficientExamples: 3x 3 is the coefficient
2x 2 is the coefficient 2x 2 is the coefficient
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Like Terms:– In an expression, like terms are
the terms that have the same variables, raised to the same powers (same exponents).•Examples: 4x and -3x or 2y2 and –y2
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• Like terms because each term consists of a single variable, x, and a numeric coefficient: 2x, 45x, x, 0x, -26x, -x
• Like terms because they are all constants: 15, -2, 27, 9043, 0.6
• Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²
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What are unlike terms?
• The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z
• Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5
• Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy
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Combine Like TermsCombine Like TermsCombine Like TermsCombine Like TermsI can simplify expressions with I can simplify expressions with
several variables by combining like several variables by combining like terms.terms.
![Page 9: Combine Like Terms](https://reader035.fdocuments.in/reader035/viewer/2022072014/56812cc3550346895d917e59/html5/thumbnails/9.jpg)
Like Terms – same variable with same exponent
6x + 2x =When combining like terms, only use the coefficients.
6x + 2x = 8x
4x + 3y – 2x + 4y =Simplify
2x + 7y
Simplify
Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.
Key Skills
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5 cats + 3 cats5 cats + 3 cats
8 cats8 cats
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5a + 3a5a + 3a
8a8a
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5 apples + 3 oranges5 apples + 3 oranges
5 apples + 3 5 apples + 3 orangesoranges
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5 cats + 3 dogs5 cats + 3 dogs
5 cats + 3 dogs5 cats + 3 dogs
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You Try• 3y + 2 + 3x – y + 5x • x + x
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Distribute by multiplication:Distribute by multiplication:
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot
complete the multiplication part of this problem.
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot
complete the multiplication part of this problem.
)43(5 n )3(5 n
)4(5
n15 20
The Distributive Property
• Expressions with variables:
Simplify 5(3n + 4).• No symbol between the 5 and the parenthesis
indicates a multiplication problem.
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The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at
this time and cannot complete the multiplication part of this problem.
The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at
this time and cannot complete the multiplication part of this problem.
6)27(4 n )7(4 n
)2(4
n28 8
6
6
n28 14
The Distributive Property
• Simplify 4(7n + 2) + 6.• No symbol between the 4 and the
parenthesis indicates a multiplication problem.
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Step 1) Use the Distributive Property 3 (2x – 5) - 2x
Step 2) Combine Like Terms 6x – 15 – 2x *** 6x and 2x are like terms!!!!
Step 3) Simplified Expression 4x – 15
Distributive Property
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Distributive PropertyExample:
6(a + 3) Use the Distributive
Property
(6a) + (6 x 3) Multiply
6a + 18 Simplified
***CAN NOT add 6a + 18 together because they are not like terms.
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Solve: 2x + 6(x + 1)
Explain how each of the below answers are wrong and why.
• 2x + 6x + 1• 9x
Practice Problems