Combining Like Terms

1. Combining Like Terms

2. 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.

3. 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.

4. How to use Algebra Tiles • Lay out the amount of algebra tiles to represent each term in the expression. • Example: 4x + 8

5. 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

6. Example 3 *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! 9x + 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  7x + 4

7. Example 4 *Change the subtraction signs to addition & make the number after the sign its opposite! 6x + 5 – 3x - 8 6x + 5 + -3x + -8 *Cross out zero pairs - 3 pairs of bars and 5 pairs of units Write your final answer out as an expression  3x - 3