Combining Like Terms

Combining Like Terms

Combining Like Terms

"Like terms" are terms whose variables are the same.

In other words, terms that are "like" each other.

Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different

Example: 7x + x

They are both like terms, so you can add them:

7x + x = 8x

By the way ... why don't we write "1x" ?

It is simpler to write x, and is so common that "1x" looks strange.

Poll

Do you see any like terms in the expressions below?

2x + 4x - 5 + 3y

• Yes

• No

The answer you should have clicked is "YES"

2x + 4x - 5 + 3y

Notice that 2x and 4x both share the same variable. Because they have the same variable, we can categorize them as "Like Terms"

To solve this, we combine like terms. 2x + 4x = 6x, therefore our answer is 6x - 5 + 3y

Multiple Select

Check all expressions below that have "like terms"

• 4x + 8x - 6

• 9y + 3y - 2

• 12a + 2ab - 3b

• 2n + 3 + 4n -3

You should have clicked on 3 out of the 4 possible answers.

Below are the 3 correct answers

4x + 8x - 6

9y + 3y - 2

2n + 3 + 4n - 3

12a + 2ab - 3b

This expression does not have like terms because 12a, 2ab, and -3b do not share the same EXACT variable(s).

(a, ab, and b, are not EXACTLY the same)

Multiple Choice

Simplify by combining like terms:

8x - 2x

• 6

• 10x

• 6x

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

6y + 3y

• 3y

• 9y²

• 9y

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

3y + 7y

• 10y

• 10y²

• 10

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

5z + z

• 5z

• 5z²

• 6z

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

9x - x

• 8x

• 9

• 8x²

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

10x + 5x - 3x - x

• 11x

• 15x

• 7x² + 2x

• They are unlike terms, so they cannot be simplified.

Poll

"Not too shabby for a bunch of 6th graders"

Do yo see any like terms in this expression?

9y² - 2y² + 8

• Yes

• No

The answer you should have clicked is "YES"

9y² - 2y² + 8

Notice that 9y² and 2y² both share the same variable (y²). Because they have the same variable, we can categorize them as "Like Terms"

To solve this, we combine like terms. 9y² - 2y² + 8, therefore our answer is

7y² + 8

Multiple Choice

Simplify by combining like terms:

10x² + 5x²

• 10x⁴

• 5x²

• 15x²

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

5a² - 3a² + 9

• 2a² + 9

• 8a² + 9

• 2a⁴ + 9

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

9n² + 3n² + 5n - 9

• 17n² + 9

• 6n² + 5n - 9

• 12n² + 5n - 9

• They are unlike terms, so they cannot be simplified.

Combine Like Terms

"Rapid Fire Edition"

See if you can get all 10 in a row right.

Multiple Choice

Simplify by combining like terms:

3x + 2x

• 5x

• x

• 6x

• 5

Multiple Choice

Simplify by combining like terms:

2x + 1 + 7x

• 10x

• 9 + 1x

• 9x + 1

• They are unlike terms, so they cannot be simplified.

Fill in the Blanks

Simplify by combining like terms: (No spaces)

12a - 5a

Fill in the Blanks

Simplify by combining like terms: (No spaces)

7y + 2y

Multiple Choice

Simplify by combining like terms:

5a + 2b - 3a + 4

• 8a + 2b + 4

• 2a + 2b + 4

• 4ab + 4

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

3x + 5y + 2xy

• 10xy

• 8xy + 2xy

• 4xy

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

2x + 1 + 7x

• 10x

• 10

• 9x + 1

• They are unlike terms, so they cannot be simplified.

Multiple Choice

Simplify by combining like terms:

7v + 2 + 12 + 2v

• 23

• 23v

• 9 + 14v

• 9v + 14

Fill in the Blanks

Simplify by combining like terms: (No spaces)

2x + 3 - x + 5

Multiple Choice

.:BONUS PROBLEM:.

Simplify the expression:

2(4 + 9w)

• 8+9w

• 2+9

• 8+18w

• They are unlike terms, so they cannot be simplified.