powerpoint overview unit 1 lesson 1.1 – simplifying expressions

Choctaw High SchoolAlgebra I EOI Review

1

Simplifying ExpressionsSimplifying Expressions

To simplify an algebraic expressions, you need to combine the like terms.

Like terms have the same variables with the same exponents.

If two terms are like terms, then only their coefficients may differ.

Once you find all the like terms, you can combine them by adding or subtracting the coefficients only.

2

An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.

Here are some examples of algebraic expressions.

3

27,7

5

3

1,4,75 2 xxyxx

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.

4

75 2 xx

7,,5 2 xx

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.

5

a ( b + c ) = ba + ca

6

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

Do you remember it?

Distributive Property

Example 1: 6(x + 2)

Distribute the 6.

6 (x + 2) = x(6) + 2(6)

= 6x + 12

Example 2: -4(x – 3)

Distribute the –4.

-4 (x – 3) = x(-4) –3(-4)

= -4x + 12

7

Try 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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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 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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Like Terms5x , -14x

-6.7xy , 02xy

The variable factors are

identical.

Unlike Terms5x , 8y

The variable factors are

not identical.

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22 8,3 xyyx

Recall 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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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

13

14

31316

terms.likeCombine

31334124

terms.theReorder

33124134

2

22

22

yxx

yxxxx

xxxyx

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 + 21

Combine like terms.- x+11

15

16

431062

1 xx

Distribute.

17

431062

1 xx

Distribute.

18

431062

1 xx

12353

3432

110

2

16

xx

xx

Distribute.

Combine like terms.

19

431062

1 xx

12353

3432

110

2

16

xx

xx

Distribute.

Combine like terms.

20

431062

1 xx

12353

3432

110

2

16

xx

xx

76 x