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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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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


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
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


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.


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.


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
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


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