How do you write equivalent expressions with variables?

1. How do you write equivalent expressions with variables? For example, how can you write an equivalent expression for 3x2 + 4x + 3?

2. In this lesson you will learn how to write equivalent expressions with variables by using a visual/area model.

3. 15 ÷ y 4a-3 We know that algebraic expressions contain numbers, operations and at least one variable. 12 - w2 2(x + 3)

4. The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products. 3(2 + 4) = (3 x 2) + (3 x 4)

5. Combining x2 and x terms.

6. What does an algebraic expression look like? Let: Stand for 1 Stand for x Stand for x2

7. We can show that the blue square represents x2 because x x x2

8. 3x2 + 4x + 3 How could you regroup these to make an equivalent expression?

9. x x x x 1 1 1 x2 x2 x2 3 x2 + 4x + 3 is equivalent to x2 + x2 + x2 + x + x + x + x + 1 + 1 + 1

10. Regroup 2x2 x2 2x 2x 3 2x2 + x2 + 2x + 2x + 3 is another way to write an equivalent expression for 3x2 + 4x + 3.

11. Let’s find two equivalent expressions for 3(x + 1) The Distributive Property can help us. 3(x + 1) = (3 • x) + (3 • 1) = 3x + 3 That’s one!

12. Let’s use the first equivalent expression to write another. 3x + 3 A drawing can help us. We can regroup these. 2x + x + 3 That’s another!

13. In this lesson you have learned how to write equivalent expressions with variables by using a visual/area model.

14. Using a drawing, write an equivalent expression for 2x2 + 2x + 2 .

15. Use drawings and the Distributive Property to help you determine which of these expressions pairs is equivalent: • 4x2 + 12 and 4(x2 + 3) • 2y +1 and 2(y + 1)

16. Use a drawing and the Distributive Property to help you write an equivalent expression for • a. 2(2x + 3) • b. 3x2 + 3x + 3 • …

17. Write two equivalent expressions for x2 + 2x + 6.

18. Write an equivalent expression for 2x2 + x + 4

19. Write an equivalent expression for 2(x + 1).