How do you write equivalent expressions with variables?

For example, how can you write an equivalent expression for 3x2 + 4x + 3?

In this lesson you will learn how to write equivalent

expressions with variables by using a visual/area model.

Let’s ReviewLet’s Review

We know that algebraic expressions contain numbers, operations and at

least one variable.

2(x + 3)

4a-3 15 ÷ y

12 - w2

Let’s ReviewLet’s ReviewThe 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)

Let’s ReviewA Common Mistake

Combining x2 and x terms.

Let’s ReviewCore LessonWhat does an algebraic expression look

like?Let:

Stand for 1

Stand for x Stand for x2

Let’s ReviewCore LessonWe can show that the blue square

represents x2 because

x

x

x2

Let’s ReviewCore Lesson

3x2 + 4x + 3

How could you regroup these to make an equivalent expression?

Let’s ReviewCore Lesson

x2 x2 x2 x x x x 1 1 1

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

1 + 1

Let’s ReviewCore Lesson Regroup

2x2 + x2 + 2x + 2x + 3 is another way to write an equivalent

expression for 3x2 + 4x + 3.

2x2 x2 2x 2x 3

Let’s ReviewCore LessonLet’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!

Let’s ReviewCore LessonLet’s use the first equivalent expression to

write another.3x + 3

A drawing can help us.We can regroup these.

2x + x

+ 3

In this lesson you have learned how to write equivalent

expressions with variables by using a visual/area model.

Let’s ReviewGuided PracticeUsing a drawing, write an equivalent expression for 2x2 + 2x + 2 .

Let’s ReviewExtension Activities

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)

Let’s ReviewExtension Activities

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

Let’s ReviewExtension Activities

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

Let’s ReviewQuick Quiz

Write an equivalent expression for 2x2 + x + 4

Let’s ReviewQuick Quiz

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