Lesson 5 CA Standard Alg 1 4.0 Simplifying Algebraic ...

[Pages:3]Lesson 5

Simplifying Algebraic Expressions

CA Standard Alg 1 4.0

An algebraic expression is a combination of numbers, operations, and one or more variables. The commutative, associative, and distributive properties are used to simplify expressions. The distributive property can be used to obtain the product of terms that contain groupings. Then, the commutative and associative properties can be used to rearrange the expression and combine the like terms.

EXAMPLE 1

1. Simplify the expression 4(x + 3) 5(x 2).

Step 1 Use the distributive property to rewrite the expressions 4(x 3) and 5(x 2).

4(x 3) (4 ? x) (4 ? 3)

5(x 2) (5 ? x) (5 ? 2)

4x 12

5x 10

Now substitute into the original expression:

4x 12 (5x 10)

Rewrite:

4x 12 (1)(5x 10)

Use the distributive property again to rewrite 1(5x 10):

1(5x 10) (1 ? 5x) (1 ? 10)

5x 10

So the expression becomes:

4x 12 5x 10

Step 2 Use the commutative property to rearrange the expression so that like terms are next to one another.

4x 5x 12 10

Step 3 Combine like terms and simplify.

1x 22 x 22

CA Standards Check 1

1a. Simplify the expression 6a(a b) 12b. 1b. Simplify the expression 9x 3(2x 2).

When using the distributive property to simplify expressions, remember that when like terms with exponents are multiplied, the exponents are added. For example, p2 ? p3 p2 3 p5.

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CA Standards Review

LESSON 5 Simplifying Algebraic Expressions 13

CA Standard Alg 1 4.0 LESSON 5

Simplifying Algebraic Expressions with Powers

When powers are present in an expression, simplify them first. Recall that like terms have the same variable raised to the same exponent. After simplifying powers and applying the distributive property (when present), combine like terms.

EXAMPLE 2

Simplify the expression 4x6 3x2(x4 1) (3x)2 5(x2 8) Step 1 Simplify the term (3x)2. 4x6 3x2(x4 1) 9x2 5(x2 + 8) Step 2 Apply the Distributive Property. 4x6 3x6 3x2 9x2 5x2 40) Step 3 Combine like terms. 7x6 7x2 40

CA Standards Check 2

2a. Simplify the expression 5p(p2 q). 2b. Simplify the expression 4y2(2y2 5) 2(y4 10).

Copyright ? Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.

14 LESSON 5 Simplifying Algebraic Expressions

CA Standards Review

Name__________________________Class____________Date________

1 Simplify the expression (4x3)2 x3(x3 2x) 3x4.

5 Which expression is equivalent to 5(r 2) (r 2)?

A 16x12 5x8 B 17x12 x8 C 17x6 x4 D 17x6 5x4

A 4r B 4r 4 C 4r 8 D 4r 12

2 Simplify the expression 4s(3st t2)

A 7s2t 5st2 B 12s2t 4st2 C 12s2t 5st2 D 48s2t 4st2

6 Simplify the expression 5 y 3(x 11).

A 3x y 28 B 3y x 28 C y 11x 15 D x 11y 15

3 Simplify the expression 2x 4(3x 2). A 10x 8 B 8x 10 C 2x 6 D 2x 6

4 Simplify the algebraic expression x y 5(y 2x). A x 4y B 9x 6y C 9x 4y D 11x 4y

7 Which algebraic expression is equivalent to 3x(x2 2) 2(x 1)?

A 3x3 2x 8 B 3x2 2x 8 C 3x3 8x 2 D 3x2 8x 2

Copyright ? Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.

CA Standards Review

LESSON 5 Simplifying Algebraic Expressions 15

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