Combining Like Terms

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# Combining Like Terms - PowerPoint PPT Presentation

Combining Like Terms. Coefficient. A coefficient is the number part of a term that includes a variable. Example: 2x 2 is the coefficient x is the variable. Constant term. Coefficients are 4 and 8. 4x + 8x +1. 4x and 8x are like terms. Combine like terms.

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### Combining Like Terms

Coefficient
• A coefficient is the number part of a term that includes a variable.
• Example: 2x
• 2 is the coefficient
• x is the variable

Constant term

Coefficients are 4 and 8

4x + 8x +1

4x and 8x are like terms

Combine like terms

+ – +

By combining apples with apples and oranges with oranges, you get...

+

like terms: terms with the same variable or variables, raised to the same power.

Like terms can be combined by adding their coefficients.

Example: What do you get when you add the fruit shown?

3 apples+ 2 oranges– 2 apples+ 2 oranges

coefficients

1 apple

+4 oranges

Only combine terms that are exactly the same!!
• What’s the “same” mean?
• If numbers have a variable, then you can combine only ones that have the same variable
• You can also combine numbers that have no variables
Examples
• Which numbers are the “same”?

5x, 8y, 9z, 10, 12x, 14z, 7

Same: 5x and 12x

Same: 10 and 7

Same: 9z and 14z

Same: 8y

Terms in an algebraic expression are separated by addition or subtraction signs.

How many terms are in this expression?

Example: Simplify 2x + 3y + 5x + 6y + 12

Find the like terms, combine their coefficients...

2x+ 3y+ 5x + 6y+ 12

7x + 9y + 12

Example: Simplify 3x – 3y – 8x – y

This is the same as 3x – 3y – 8x – 1y

= – 5x – 4y

Example:

Reorder the terms.

Combine like terms.

Combine like terms.

A.14a – 5a

Identify like terms.

9a

Combine coefficients: 14 – 5 = 9

Identify like terms ; the coefficient of y is 1, because 1y = y.

B.7y + 8 – 3y – 1 + y

Combine coefficients:

7 – 3 + 1 = 5 and 8 – 1 = 7

5y + 7

Combine like terms.

Identify like terms; the coefficient of q is 1, because 1q = q.

C.4q – q

3q

Combine coefficients: 4 – 1 = 3

Identify like terms; the coefficient of c is 1, because 1c = c.

D.5c + 8– 4c – 2 – c

Combine coefficients:

5 – 4 – 1 = 0 and 8 – 2 = 6

6

Combine like terms.

E. 4m + 9n – 2

4m + 9n – 2

No like terms.

F. 5m – 7m – 8 + 4

-2m – 4

Remember, to simplify an expression means to perform all possible operations, including combining like terms.

In other words, simplify means solve!

Final Problems:

1. 4x + 5y – 2x + 3y

2. 5x + 5y + 2x + 2y

3. 3 + 5x – 4y + 2y – 8x

2x + 8y

7x + 7y

3 – 3x – 2y

Practice:

worksheet