Combining Like Terms

Combining Like Terms

Vocabulary• When an operation separates an algebraic expression into

parts, each part is called a term.– Example: 2x + 5 2x and 5 are both terms

• Like terms contain the same variables and powers. – Example: 2x + 5 + x

• 2x & x are like terms because they both contain the variable x.• The power that the variables have in this problem is 1.

– Example: 2x² + 5 + x• 2x² and x do not have the same power, so they would not be like

terms.

• A term without a variable is called a constant. Constant terms are also like terms.– Example: 5 + 2x + 6

• 5 and 6 are constants, which means they are also like terms.

Algebra Tiles• Blue/Red Squares – represent variables squared

– Examples: x², y², -a², b², …..

• Green/Red Bars – represent variables– Examples: x, y, a, -b, …

• White/Red Units – represent constants– Examples: 5, 9, -8, 27, …

• The red side of all of these tiles represents negative and the blue, green, and white sides represent positive.

How to use Algebra Tiles

• Lay out the amount of algebra tiles to represent each term in the expression.

• Example:

4x + 8

Let’s try another example• Example 2:

6x + 5 + 2x

• Explain what you see with your tiles.

– 8 green bars, and 5 white units.

• Can you write that out as an expression?

– 8x + 5

Example 39x + 4 – 2x

9x + 4 + -2x

If I count up what I have. What do you think the green and red bars will do?

– Cancel each other out & make ZERO PAIRS!

– There are two zero pairs that you can make!

• Write your final answer out as an expression

*I don’t know how to show subtracting 2x.

*What you can do is change the problem to addition and make the number after the sign it’s opposite!

7x + 4

Example 4

6x + 5 – 3x - 8

6x + 5 + -3x + -8

*Change the subtraction signs to addition & make the number after the sign its opposite!

*Cross out zero pairs

Write your final answer out as an expression 3x - 3

- 3 pairs of bars and 5 pairs of units