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This pdf contains the following topics:-

Distributive property

Coefficient

Combining Like Terms

Simplify by combining like terms.

Examples and many more

Distributive property

Coefficient

Combining Like Terms

Simplify by combining like terms.

Examples and many more

1.
1-7 Simplifying Expressions

Warm Up

Add.

1. 427 + 35 462 2. 1.06 + 0.74 1.80

3. 10

Multiply.

4. 25(8) 200 5. 1.3(22) 28.6

6.

Holt Algebra 1

Warm Up

Add.

1. 427 + 35 462 2. 1.06 + 0.74 1.80

3. 10

Multiply.

4. 25(8) 200 5. 1.3(22) 28.6

6.

Holt Algebra 1

2.
1-7 Simplifying Expressions

The Distributive Property is used with Addition to

Simplify Expressions.

The Distributive Property also works with

subtraction because subtraction is the same as

adding the opposite.

Holt Algebra 1

The Distributive Property is used with Addition to

Simplify Expressions.

The Distributive Property also works with

subtraction because subtraction is the same as

adding the opposite.

Holt Algebra 1

3.
1-7 Simplifying Expressions

The terms of an expression are the parts to be

added or subtracted. Like terms are terms that

contain the same variables raised to the same

powers. Constants are also like terms.

Like terms Constant

4x – 3x + 2

Holt Algebra 1

The terms of an expression are the parts to be

added or subtracted. Like terms are terms that

contain the same variables raised to the same

powers. Constants are also like terms.

Like terms Constant

4x – 3x + 2

Holt Algebra 1

4.
1-7 Simplifying Expressions

A coefficient is a number multiplied by a

variable. Like terms can have different

coefficients. A variable written without a

coefficient has a coefficient of 1.

Coefficients

1x2 + 3x

Holt Algebra 1

A coefficient is a number multiplied by a

variable. Like terms can have different

coefficients. A variable written without a

coefficient has a coefficient of 1.

Coefficients

1x2 + 3x

Holt Algebra 1

5.
1-7 Simplifying Expressions

Using the Distributive Property can help you

combine like terms. You can factor out the

common factors to simplify the expression.

7x2 – 4x2 = (7 – 4)x2 Factor out x2 from both terms.

= (3)x2 Perform operations in

parenthesis.

= 3x2

Notice that you can combine like terms by

adding or subtracting the coefficients and

keeping the variables and exponents the same.

Holt Algebra 1

Using the Distributive Property can help you

combine like terms. You can factor out the

common factors to simplify the expression.

7x2 – 4x2 = (7 – 4)x2 Factor out x2 from both terms.

= (3)x2 Perform operations in

parenthesis.

= 3x2

Notice that you can combine like terms by

adding or subtracting the coefficients and

keeping the variables and exponents the same.

Holt Algebra 1

6.
1-7 Simplifying Expressions

Example 3A: Combining Like Terms

Simplify the expression by combining like

terms.

72p – 25p

72p – 25p 72p and 25p are like terms.

47p Subtract the coefficients.

Holt Algebra 1

Example 3A: Combining Like Terms

Simplify the expression by combining like

terms.

72p – 25p

72p – 25p 72p and 25p are like terms.

47p Subtract the coefficients.

Holt Algebra 1

7.
1-7 Simplifying Expressions

Example 3B: Combining Like Terms

Simplify the expression by combining like

terms.

A variable without a coefficient

has a coefficient of 1.

and are like terms.

Write 1 as .

Add the coefficients.

Holt Algebra 1

Example 3B: Combining Like Terms

Simplify the expression by combining like

terms.

A variable without a coefficient

has a coefficient of 1.

and are like terms.

Write 1 as .

Add the coefficients.

Holt Algebra 1

8.
1-7 Simplifying Expressions

Example 3C: Combining Like Terms

Simplify the expression by combining like

terms.

0.5m + 2.5n

0.5m + 2.5n 0.5m and 2.5n are not like terms.

0.5m + 2.5n Do not combine the terms.

Holt Algebra 1

Example 3C: Combining Like Terms

Simplify the expression by combining like

terms.

0.5m + 2.5n

0.5m + 2.5n 0.5m and 2.5n are not like terms.

0.5m + 2.5n Do not combine the terms.

Holt Algebra 1

9.
1-7 Simplifying Expressions

Check It Out! Example 3

Simplify by combining like terms.

3a. 16p + 84p

16p + 84p 16p + 84p are like terms.

100p Add the coefficients.

3b. –20t – 8.5t2

–20t – 8.5t2 20t and 8.5t2 are not like terms.

–20t – 8.5t2 Do not combine the terms.

3c. 3m2 + m3

3m2 + m3 3m2 and m3 are not like terms.

3m2 + m3 Do not combine the terms.

Holt Algebra 1

Check It Out! Example 3

Simplify by combining like terms.

3a. 16p + 84p

16p + 84p 16p + 84p are like terms.

100p Add the coefficients.

3b. –20t – 8.5t2

–20t – 8.5t2 20t and 8.5t2 are not like terms.

–20t – 8.5t2 Do not combine the terms.

3c. 3m2 + m3

3m2 + m3 3m2 and m3 are not like terms.

3m2 + m3 Do not combine the terms.

Holt Algebra 1

10.
1-7 Simplifying Expressions

Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

Procedure Justification

1. 14x + 4(2 + x)

2. 14x + 4(2) + 4(x) Distributive Property

3. 14x + 8 + 4x Multiply.

4. 14x + 4x + 8 Commutative Property

5. (14x + 4x) + 8 Associative Property

6. 18x + 8 Combine like terms.

Holt Algebra 1

Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

Procedure Justification

1. 14x + 4(2 + x)

2. 14x + 4(2) + 4(x) Distributive Property

3. 14x + 8 + 4x Multiply.

4. 14x + 4x + 8 Commutative Property

5. (14x + 4x) + 8 Associative Property

6. 18x + 8 Combine like terms.

Holt Algebra 1

11.
1-7 Simplifying Expressions

Check It Out! Example 4a

Simplify 6(x – 4) + 9. Justify each step.

Procedure Justification

1. 6(x – 4) + 9

2. 6(x) – 6(4) + 9 Distributive Property

3. 6x – 24 + 9 Multiply.

Combine like terms.

4. 6x – 15

Holt Algebra 1

Check It Out! Example 4a

Simplify 6(x – 4) + 9. Justify each step.

Procedure Justification

1. 6(x – 4) + 9

2. 6(x) – 6(4) + 9 Distributive Property

3. 6x – 24 + 9 Multiply.

Combine like terms.

4. 6x – 15

Holt Algebra 1

12.
1-7 Simplifying Expressions

Check It Out! Example 4b

Simplify −12x – 5x + 3a + x. Justify each step.

Procedure Justification

1. –12x – 5x + 3a + x

2. –12x – 5x + x + 3a Commutative Property

3. –16x + 3a Combine like terms.

Holt Algebra 1

Check It Out! Example 4b

Simplify −12x – 5x + 3a + x. Justify each step.

Procedure Justification

1. –12x – 5x + 3a + x

2. –12x – 5x + x + 3a Commutative Property

3. –16x + 3a Combine like terms.

Holt Algebra 1

13.
1-7 Simplifying Expressions

Lesson Quiz: Part II

Simplify each expression by combining like

terms. Justify each step with an operation or

property.

5.

6. 14c2 – 9c 14c2 – 9c

7. 301x – x 300x

8. 24a + b2 + 3a + 2b2 27a + 3b2

Holt Algebra 1

Lesson Quiz: Part II

Simplify each expression by combining like

terms. Justify each step with an operation or

property.

5.

6. 14c2 – 9c 14c2 – 9c

7. 301x – x 300x

8. 24a + b2 + 3a + 2b2 27a + 3b2

Holt Algebra 1