Combining Like Terms Students will identify like terms

Combining Like Terms Students will identify like terms and combine like terms to solve problems.

Combine Like Fruits 4 apples + 3 bananas 4 + 3 apples 7 apples + 3 apples 3 + 2 bananas 5 bananas + 2 bananas

Only combine terms that are the same!! • What’s the “SAME” or “Like Terms” mean? – The variables (letters) MUST be the same with the SAME POWERS. – You can also combine numbers that have no variables.

Examples Which terms are the “same” or LIKE TERMS? TERMS 5 x, 8 y, 9 z, 10, x 2, 12 x, 14 z, 7, 3 x 2 5 x and ? 12 x 8 y and ? NOTHING! 9 z and ? 14 z 10 and ? 7 x 2 and ? 3 x 2

Combining Terms To combine Like Terms, add or subtract the coefficients (numbers in front of the variables)… The variable stays the same. Example: 5 x + 9 x THINK: 5 + 9 = 14 and bring down the x. 14 x

Let’s try it! 4 x + 9 x 13 x 4 x + 8 y + 10 x 14 x + 8 y -7 y + 9 y 2 y -8 y + (-4 y) -12 y 5 + 8 x + 7 y + 10 8 x + 7 y + 15

More Problems: 1. 4 x + 5 y – 2 x + 3 y 2 x + 8 y 2. 5(x + y) + 2(x + y) Use the distributive property first. 5 x + 5 y + 2 x + 2 y 7 x + 7 y 3. 3 + 5 x – 4 y + 2 y – 8 x 3 – 3 x – 2 y

Problems Cont. 4. (-13) + (-2 y) + (-7) – 4 y -20 – 6 y 5. 8(2 x – 3 y) + 4(y – 3 x) 16 x – 24 y + 4 y – 12 x 4 x – 20 y

Summary Combine LIKE TERMS only if they have exactly the same letters with the same powers. Combine Like Terms by adding or subtracting the coefficients (numbers) Constants (terms without variables) can also be combined by adding or subtracting. END