The Distributive PropertyThe Distributive Property

Chapter 1 Lesson 4Chapter 1 Lesson 4

Try these problems:Try these problems:

1. 3 * (4 * x)

2. 4 + s + 7

3. 7 * m * 2

4. 3 * (4 + x)

1. 3 * (4 * x)

2. 4 + s + 7

3. 7 * m * 2

4. 3 * (4 + x)

The Distributive PropertyThe Distributive PropertyDefinition:

Symbols:

Example:

Mental MathMental Math

You can use the distributive property when doing mental math!!!

Multiply 8 * 12 mentally.

You can use the distributive property when doing mental math!!!

Multiply 8 * 12 mentally.

ExamplesExamples

1. 3 (x + 7) 2. 5(2n + 8)

3. 6(a + b) 4. (1 + 3t)9

1. 3 (x + 7) 2. 5(2n + 8)

3. 6(a + b) 4. (1 + 3t)9

A way to remember….A way to remember….

You can think of the distributive property as a rainbow.

3 ( 2t - 2)

You can think of the distributive property as a rainbow.

3 ( 2t - 2)

Words to Remember:Words to Remember:

Term: A term can be a _______________, _______________, _________________ or ____________________ of numbers and variables. How do you know how many terms are in an

expression? Terms are separated by __________ or ________

signs.

Term: A term can be a _______________, _______________, _________________ or ____________________ of numbers and variables. How do you know how many terms are in an

expression? Terms are separated by __________ or ________

signs.

More Words to RememberMore Words to Remember Like Terms: Terms that contain the same

___________________. Example of like terms:

Coefficient: The _____________ part of a term that contains a variable.

Equivalent Expressions: Two or more expressions that have the same _________.

Simplest Form: An algebraic expression is in simplest form when it has no _________ _______ and no __________________.

Like Terms: Terms that contain the same ___________________. Example of like terms:

Coefficient: The _____________ part of a term that contains a variable.

Equivalent Expressions: Two or more expressions that have the same _________.

Simplest Form: An algebraic expression is in simplest form when it has no _________ _______ and no __________________.

PracticePractice

Determine how many terms are in each expression.

1. 3x + 4xy + 2 2. 4 + m + 3n + 2

3. 4xy - x 4. 4b

5. 3 - x 6. 2xy + 3 - 4y + 7 - 3x

Determine how many terms are in each expression.

1. 3x + 4xy + 2 2. 4 + m + 3n + 2

3. 4xy - x 4. 4b

5. 3 - x 6. 2xy + 3 - 4y + 7 - 3x

For each expression, circle each pair of like terms. If there are two sets of like terms, circle one pair and underline the

second.

For each expression, circle each pair of like terms. If there are two sets of like terms, circle one pair and underline the

second. 7. 8c + 11 - 6c 8. 15d - 9 + 2d

9. 7q + 2z + q + 5z 10. 6 + 2rs - 5

11. 9f + 9g 12. 8 + 5z - 6 + z

7. 8c + 11 - 6c 8. 15d - 9 + 2d

9. 7q + 2z + q + 5z 10. 6 + 2rs - 5

11. 9f + 9g 12. 8 + 5z - 6 + z

Determine the coefficient of each underlined term.

Determine the coefficient of each underlined term.

13. 3x + 4y - 5 14. 8 + 5z - 6 + z

15. 3y - 5 + 2y 16. 3 + 5x - 2

17. 4y - 2 + y

13. 3x + 4y - 5 14. 8 + 5z - 6 + z

15. 3y - 5 + 2y 16. 3 + 5x - 2

17. 4y - 2 + y

Match the expression on the left with its

equivalent expression on the right. Match the expression on the left with its

equivalent expression on the right.

18. 5x + 3 - 2x A. 7 + y

19. 4 + y + 3 B. 7w + 6

20. 8 + 5z - 6 + z C. 3x + 3

21. 2 + 7q + 3r + q D. 2 + 6z

22. w + 10 - 4 + 6w E. 8q + 3r + 2

18. 5x + 3 - 2x A. 7 + y

19. 4 + y + 3 B. 7w + 6

20. 8 + 5z - 6 + z C. 3x + 3

21. 2 + 7q + 3r + q D. 2 + 6z

22. w + 10 - 4 + 6w E. 8q + 3r + 2

Circle the column above in which all expressions are simplified.

Explain in your own words how you know that an expression is in

its simplest form.

Explain in your own words how you know that an expression is in

its simplest form.