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
Review
Let’s
Review
We know that algebraic expressions
contain numbers, operations and at
least one variable.
Let’s
Review
Let’s
Review
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)
A Common
Let’s
Review Mistake
Combining x2 and x terms.
CoreReview
Lesson
Let’s
What does an algebraic expression
look like?
Let:
Stand for
1
Stand for x
Stand for x2
CoreReview
Lesson
Let’s
We can show that the blue square
represents x2 because
x
x
x2
CoreReview
Lesson
Let’s
3x2 + 4x + 3
How could you regroup these to
make an equivalent expression?
CoreReview
Lesson
Let’s
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
CoreReview
Lesson
Let’s
2x2
Regroup
x2
2x
2x
3
2x2 + x2 + 2x + 2x + 3
is another way to write an equivalent
expression for 3x2 + 4x + 3.
CoreReview
Lesson
Let’s
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!
CoreReview
Lesson
Let’s
Let’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.
Guided
Practice
Let’s
Review
Using a drawing, write an equivalent
expression for 2x2 + 2x + 2 .
Extension
Let’s
ReviewActivities
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)
Extension
Let’s
ReviewActivities
Use a drawing and the Distributive
Property to help you write an equivalent
expression for
a. 2(2x + 3)
b. 3x2 + 3x + 3
…
Extension
Let’s
ReviewActivities
Write two equivalent expressions for
x2 + 2x + 6.
Quick Quiz
Let’s
Review
Write an equivalent expression for
2x2 + x + 4
Quick Quiz
Let’s
Review
Write an equivalent expression for
2(x + 1).