Properties
3x + 8
8 + 3x
Commutative Property
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
3x + 2x + 5x
10x
What does the word "substitution" mean?
Replace/take the place
3x - 9 = 3(x - 3)
Distributive Property
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
20x + 20 - 8x + 8
12x + 28
If a = 5 and b= 8, what does the following expression simplify to?
9a - 5b
2x + (3x + 8) = (2x + 3x) + 8
Associative Property
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)
45x2 + 47x + 42x - 2x2
43x2 + 89x
Use substitution to determine if the following are equal or not equal:
x3 + 3y ______ x + x + x + y + y + y
-4 + 4 = 0
Additive Inverse Property
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
10n + 5 - 5n + 3 + 5n
10n + 8
Use substitution to determine if the following are equal:
5m + 10n - j2 __________ 5 (m + 2n) - j * j
=
Factor out a number to make an equivalent expression:
20x + 8
Hint: Put it in this form - ___ (___ + ____)
2(10x + 4)
4(5x + 2)
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
3(2y - 8) - 4y + 12
2y - 12
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.