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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.

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Presentation Transcript
coefficient
Coefficient
  • A coefficient is the number part of a term that includes a variable.
  • Example: 2x
  • 2 is the coefficient
  • x is the variable
slide3

Constant term

Coefficients are 4 and 8

4x + 8x +1

4x and 8x are like terms

slide4

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
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
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

slide7

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

How many terms are in this expression?

The sign in front of each coefficient goes with that term.

slide8

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
Example:

Reorder the terms.

Combine like terms.

slide10

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

slide11

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

slide12

Combine like terms.

E. 4m + 9n – 2

4m + 9n – 2

No like terms.

F. 5m – 7m – 8 + 4

-2m – 4

slide13

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

In other words, simplify means solve!

final problems
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

slide15

Practice:

worksheet

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