Equivalent Expressions

Properties

Combining Like-Terms

Substitution

100

3x + 8

8 + 3x

Commutative Property

100

Which of the following are equal to each other?

A. 2x + 7

B. 2(x + 7)

C. 2x + 14

D. x + 2x + 3 + 4

B. 2(x + 7) and C. 2x + 14

100

3x + 2x + 5x

10x

100

What does the word "substitution" mean?

Replace/take the place

200

3x - 9 = 3(x - 3)

Distributive Property

200

Which of the following are equal to each other?

A. 4xy

B. 2x + 2y

C. 2(x + 1)

D. x + x + y + y

B. 2x + 2y and D. x + x + y + y

200

20x + 20 - 8x + 8

12x + 28

200

If a = 5 and b= 8, what does the following expression simplify to?

9a - 5b

300

2x + (3x + 8) = (2x + 3x) + 8

Associative Property

300

Which of the following are equal to each other?

A. 4z + 16

B. 4(z + 4)

C. 4(z + 16)

D. z*z*z*z + 16

A. 4z + 16 and B. 4(z + 4)

300

45x² + 47x + 42x - 2x²

43x² + 89x

300

Use substitution to determine if the following are equal or not equal:

x³ + 3y ______ x + x + x + y + y + y

They are not equal.

400

-4 + 4 = 0

Additive Inverse Property

400

Which of the following are equal to each other?

A. 2(3a + 6)

B. 6(a + 2)

C. 6a + 12

D. 3a + 2a + 10 + 2

A. 2(3a + 6), B. 6(a + 2), and C. 6a + 12

400

10n + 5 - 5n + 3 + 5n

10n + 8

400

Use substitution to determine if the following are equal:

5m + 10n - j² __________ 5 (m + 2n) - j * j

500

Factor out a number to make an equivalent expression:

20x + 8

Hint: Put it in this form - ___ (___ + ____)

2(10x + 4)

4(5x + 2)

500

Which of the following are equal to each other?

A. 3y - 6

B. 6 - 3y

C. 3(y - 2)

D. -6 + 3y

A. 3y - 6, C. 3(y - 2), and D. -6 + 3y

500

3(2y - 8) - 4y + 12

2y - 12

500

Tyler determined that the following expressions were equal when he substituted 1 in for x. Do you agree with Tyler? Why or why not?

x³ + 4x + 12 ________ 4 (x + 3) + x⁴

No. They appeared to be equal because 1 to the 3 power and 1 to the 4th power both equal 1. However, if you use any other number there (besides 0), this will prove that they are not equal.