2 ObjectiveThis presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.
3 Algebraic Expressions An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.Here are some examples of algebraic expressions.
4 Consider the example:The terms of the expression are separated by addition. There are 3 terms in this example and they areThe 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.
5 Let’s 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.
6 Distributive Property To simplify some expressions we may need to use the Distributive PropertyDo you remember it?Distributive Propertya ( b + c ) = ba + ca
8 Practice Problem Try the Distributive Property on -7 ( x – 2 ) . Be sure to multiply each term by a –7.-7 ( x – 2 ) = x(-7) – 2(-7)= -7xNotice when a negative is distributed all the signs of the terms in the ( )’s change.
9 Examples with 1 and –1. Example 3: (x – 2) = 1( x – 2 ) = x(1) – 2(1) 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 + 3Notice that multiplying by a –1 changes the signs of each term in the ( )’s.
10 Like TermsLike 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.
11 Examples Like Terms 5x , -14x -6.7xy , 02xy The variable factors are identical.Unlike Terms5x , 8yThe variable factors arenot identical.
12 Combining Like Terms Recall the Distributive Property a (b + c) = b(a) +c(a)To see how like terms are combined use theDistributive Property in reverse.5x + 7x = x (5 + 7)= x (12)= 12x
13 Example All that work is not necessary every time. Simply identify the like terms and add theircoefficients.4x + 7y – x + 5y = 4x – x + 7y +5y= 3x + 12y
15 Both Skills This 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
19 Simplifying ExampleDistribute.Combine like terms.
20 Simplifying ExampleDistribute.Combine like terms.
21 Evaluating Expressions 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.Remember to use correct order of operations.
22 Example Evaluate 2x–3xy +4y when x = 3 and y = -5. Substitute in the numbers.2(3) – 3(3)(-5) + 4(-5)Use correct order of operations.– 2051 – 2031