Simplifying Expressions.ppt

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  • Simplifying ExpressionsBy: Karen Overman

  • Objective This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.

  • Algebraic ExpressionsAn algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.

    Here are some examples of algebraic expressions.

  • 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.

  • 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.

  • Distributive Propertya ( b + c ) = ba + ca

    To simplify some expressions we may need to use the Distributive Property

    Do you remember it?

    Distributive Property

  • 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

  • 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.

  • 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.

  • 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.

  • ExamplesLike Terms5x , -14x

    -6.7xy , 02xy

    The variable factors areidentical.Unlike Terms5x , 8y

    The variable factors are not identical.

  • 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

  • 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

  • Collecting Like Terms Example

  • 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

  • Simplifying Example

  • Simplifying Example

    Distribute.

  • Simplifying Example

    Distribute.

  • Simplifying Example

    Distribute.

    Combine like terms.

  • Simplifying Example

    Distribute.

    Combine like terms.

  • 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.

  • 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

  • Evaluating Example

  • Evaluating Example

    Substitute in the numbers.

  • Evaluating Example

    Substitute in the numbers.

  • Evaluating ExampleRemember correct order of operations.Substitute in the numbers.

  • Common MistakesIncorrect

    Correct