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 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 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 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 x 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 3 9x + 4 – 2x 9x x 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 x + -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 pairs of barsand 5 pairs of units