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This pdf includes the following topics:-

Algebraic expression

Like Terms

Unlike Terms

The Commutative Property

The Associative Property

The Distributive Property

Algebraic expression

Like Terms

Unlike Terms

The Commutative Property

The Associative Property

The Distributive Property

1.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

Simplifying Algebraic Expressions

1

Simplifying Algebraic Expressions

1

2.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

Algebraic expression: a combination of

numbers, letters (variables), and operation

symbols

Examples:

4x n+7 3y 5 x

How do you read each of the expressions

above?

2

Algebraic expression: a combination of

numbers, letters (variables), and operation

symbols

Examples:

4x n+7 3y 5 x

How do you read each of the expressions

above?

2

3.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

The addends of an algebraic expression are

called the terms of the expression.

x+3

2 terms

3y2 6y + 4

3 terms

constant: a number without a variable

variable term: a term with a variable

coefficient: the number in front of a variable

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The addends of an algebraic expression are

called the terms of the expression.

x+3

2 terms

3y2 6y + 4

3 terms

constant: a number without a variable

variable term: a term with a variable

coefficient: the number in front of a variable

3

4.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

LIKE TERMS have the same variable factors

but can have different coefficients

Like Terms: Unlike Terms:

3x, 4x 5x, x2

6y, 2y, y 7x, 7y

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LIKE TERMS have the same variable factors

but can have different coefficients

Like Terms: Unlike Terms:

3x, 4x 5x, x2

6y, 2y, y 7x, 7y

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5.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

True or False? The following terms are like

terms.

1. 3x & 3y

2. 5x & 9x

3. 2x2 & 2y2

4. 7xz2 & 3z2x

5

True or False? The following terms are like

terms.

1. 3x & 3y

2. 5x & 9x

3. 2x2 & 2y2

4. 7xz2 & 3z2x

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6.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

Like terms can be combined when using the

properties of numbers. The properties help

us to simplify expressions.

An algebraic expression is simplified when

all like terms have been combined.

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Like terms can be combined when using the

properties of numbers. The properties help

us to simplify expressions.

An algebraic expression is simplified when

all like terms have been combined.

6

7.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

The Commutative Property:

Addition:

a+b=b+a

Multiplication:

ab = ba

*The ORDER of adding or multiplying two

numbers can be changed without changing

their sum or product*

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The Commutative Property:

Addition:

a+b=b+a

Multiplication:

ab = ba

*The ORDER of adding or multiplying two

numbers can be changed without changing

their sum or product*

7

8.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

EXAMPLES:

1. 2 + 3 = 3 + 2

2. 7(9) = 9(7)

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EXAMPLES:

1. 2 + 3 = 3 + 2

2. 7(9) = 9(7)

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9.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

The Associative Property:

Addition:

(a + b) + c = a + (b + c)

Multiplication:

(ab)c = a(bc)

The GROUPING of numbers in addition or

multiplication can be changed without

changing their sum or product.

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The Associative Property:

Addition:

(a + b) + c = a + (b + c)

Multiplication:

(ab)c = a(bc)

The GROUPING of numbers in addition or

multiplication can be changed without

changing their sum or product.

9

10.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

EXAMPLES:

1. (1 + 8) + 10 = 1 + (8 + 10)

2. (4 2) 3 = 4 (2 3)

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EXAMPLES:

1. (1 + 8) + 10 = 1 + (8 + 10)

2. (4 2) 3 = 4 (2 3)

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11.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

The Distributive Property:

If a, b, and c are numbers, then...

Addition: Subtraction:

a(b + c) = ab + ac a(b c) = ab ac

or or

(a + b)c = ac + bc (a b)c = ac bc

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The Distributive Property:

If a, b, and c are numbers, then...

Addition: Subtraction:

a(b + c) = ab + ac a(b c) = ab ac

or or

(a + b)c = ac + bc (a b)c = ac bc

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Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

EXAMPLES:

1. 2(x + 3)

2. (y 1)5

3. (7 + 2)x

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EXAMPLES:

1. 2(x + 3)

2. (y 1)5

3. (7 + 2)x

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13.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

Use the properties of numbers for addition to

simplify each expression by combining like

terms.

1. 4x + 6x 4. 2y 6 + 4y + 8

2. y 5y 5. 2x 5 + 3y + 4x 10y + 11

3. 3x2 + 5x2 2

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Use the properties of numbers for addition to

simplify each expression by combining like

terms.

1. 4x + 6x 4. 2y 6 + 4y + 8

2. y 5y 5. 2x 5 + 3y + 4x 10y + 11

3. 3x2 + 5x2 2

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14.
Lesson 6Simplifying Algebraic Expressions.notebook August 28, 2017

Use the properties of numbers for multiplication

to simplify each expression by combining like

terms.

1. 5(3y) 4. 3(5a + 2)

2. 2(4x) 5. 8(x 4)

3. 5(x + 4)

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Use the properties of numbers for multiplication

to simplify each expression by combining like

terms.

1. 5(3y) 4. 3(5a + 2)

2. 2(4x) 5. 8(x 4)

3. 5(x + 4)

14