Simplifying Expressions.ppt
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Transcript of Simplifying Expressions.ppt
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Simplifying ExpressionsBy: Karen Overman
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Objective This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.
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Algebraic ExpressionsAn algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.
Here are some examples of algebraic expressions.
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Consider the example: The terms of the expression are separated by addition. There are 3 terms in this example and they are .
The coefficient of a variable term is the real number factor. The first term has coefficient of 5. The second term has an unwritten coefficient of 1.
The last term , -7, is called a constant since there is no variable in the term.
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Lets begin with a review of two important skills for simplifying expression, using the Distributive Property and combining like terms. Then we will use both skills in the same simplifying problem.
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Distributive Propertya ( b + c ) = ba + ca
To simplify some expressions we may need to use the Distributive Property
Do you remember it?
Distributive Property
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ExamplesExample 2: -4(x 3)Distribute the 4.
-4 (x 3) = x(-4) 3(-4) = -4x + 12Example 1: 6(x + 2)Distribute the 6.
6 (x + 2) = x(6) + 2(6) = 6x + 12
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Practice ProblemTry the Distributive Property on -7 ( x 2 ) . Be sure to multiply each term by a 7.
-7 ( x 2 ) = x(-7) 2(-7) = -7x + 14
Notice when a negative is distributed all the signs of the terms in the ( )s change.
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Examples with 1 and 1.Example 3: (x 2)
= 1( x 2 )
= x(1) 2(1)
= x - 2
Notice multiplying by a 1 does nothing to the expression in the ( )s.
Example 4: -(4x 3)
= -1(4x 3)
= 4x(-1) 3(-1)
= -4x + 3
Notice that multiplying by a 1 changes the signs of each term in the ( )s.
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Like Terms Like terms are terms with the same variables raised to the same power.
Hint: The idea is that the variable part of the terms must be identical for them to be like terms.
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ExamplesLike Terms5x , -14x
-6.7xy , 02xy
The variable factors areidentical.Unlike Terms5x , 8y
The variable factors are not identical.
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Combining Like TermsRecall the Distributive Propertya (b + c) = b(a) +c(a)To see how like terms are combined use the Distributive Property in reverse.5x + 7x = x (5 + 7) = x (12) = 12x
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Example All that work is not necessary every time.Simply identify the like terms and add their coefficients.
4x + 7y x + 5y = 4x x + 7y +5y = 3x + 12y
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Collecting Like Terms Example
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Both SkillsThis example requires both the Distributive Property and combining like terms.5(x 2) 3(2x 7)Distribute the 5 and the 3.x(5) - 2(5) + 2x(-3) - 7(-3) 5x 10 6x + 21Combine like terms.- x+11
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Simplifying Example
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Simplifying Example
Distribute.
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Simplifying Example
Distribute.
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Simplifying Example
Distribute.
Combine like terms.
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Simplifying Example
Distribute.
Combine like terms.
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Evaluating ExpressionsRemember to use correct order of operations.Evaluate the expression 2x 3xy +4y whenx = 3 and y = -5.
To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number.
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ExampleEvaluate 2x3xy +4y when x = 3 and y = -5.Substitute in the numbers.2(3) 3(3)(-5) + 4(-5)Use correct order of operations.6 + 45 20 51 2031
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Evaluating Example
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Evaluating Example
Substitute in the numbers.
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Evaluating Example
Substitute in the numbers.
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Evaluating ExampleRemember correct order of operations.Substitute in the numbers.
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Common MistakesIncorrect
Correct