Distributive property
Simplify:
-3(5x-4)
-15x+12
Simplify:
3(2)+6a=2(a)
4a+6
Commutative Property
The order of the numbers don't matter in addition or multiplication.
If point A, (3,-4) is translated 2 units up, what is A'?
(3,-2)
Evaluate:
8b + 3 if b=2
19
Simplify:
-2(2a-4d)+4f
-4a+8d+4f
Simplify:
4(2x-3)=a(5)
-5a+8x-12
Distributive Property
Multiplying a sum by a number is the same as multiplying each addend by that same number.
If point A, (2,-3) is translated 4 units to the left, what is A'?
(-2,-3)
Evaluate:
2b + 3c -4 if b=3 and c=-2
-4
Simplify:
2(3z+1)-2(5+z)
4z-8
Simplify:
12x+3a=2(c)+x
3a-2c+11x
Identity Property
When you multiply a number by 1 or add 0 the number stays the same.
If point A, (5,1) is translated 1 unit up and 2 units right, what is A'?
(7,2)
Evaluate:
7x - 4v - b(4) if x=3, v=-2, and b=-4.
45
Simplify:
3(c-2d)-2(2c-3d)
-c
Simplify:
5(2z-6a)=5(2+z)+a
31a-5z+10
Associative Property
The way you group numbers for addition or multiplication doesn't matter.
If point A, (-3,-1) is translated 5 units up and 6 units to the right, what is A'?
(3,4)
Evaluate:
z(b-a) + 2(ab) if z=3, b=2, and a=-5
-29
Simplfiy:
2m^2(5m^3-2m+1)
10m^5-4m^3+2m^2
Simplify:
-4.1 - 5x^2 - 8.6x + 3.05x + 8.1y^2 - 21.4x^2 + 3.2
-26.4x^2 - 5.55x + 8.1y^2 - 0.9
Inverse Property
Adding an opposite of a number results in getting 0 while multiplying it by its reciprocal results in 1.
If point A, (8,-2), is translated 12 units up and 4 units to the left, what is A'?
(4,10)
Evaluate:
ab(f - 3)(z) if a=3, b=5, f=-2, and z=2.
-150