Distributive property
Simplify:
-3(5x-4)
-3(5x-4)
-3(5x)+-3(-4)
-15x+12
-15x+12
Simplify:
3(2)+6a=2(a)
3(2)+6a=2(a)
6+6a=2a
-2a -2a
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,-4+2)
(3,-2)
Evaluate:
8b + 3 if b=2
8(2) + 3
16 + 3
19
Simplify:
-2(2a-4d)+4f
-2(2a-4d)+4f
-2(2a)+(-2)(-4d)+4f
-4a+8d+4f
Simplify:
4(2x-3)=a(5)
4(2x-3)=a(5)
4(2x)+4(-3)=a(5)
8x-12=5a
-5a -5a
-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'?
(2-4,-3)
(-2,-3)
Evaluate:
2b + 3c -4 if b=3 and c=-2
2(3) + 3(-2) - 4
6 - 6 - 4
0 - 4
Simplify:
2(3z+1)-2(5+z)
2(3z+1)-2(5+z)
2(3z)+2(1)-2(5)-2(z)
6z+2-10-2z
4z-8
Simplify:
12x+3a=2(c)+x
12x+3a=2(c)+x
12x+3a=2c+x
-2c -x -2c -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'?
(5+2,1+1)
(7,2)
Evaluate:
7x - 4v - b(4) if x=3, v=-2, and b=-4.
7(3) - 4(-2) - (-4)(4)
21+8+16
45
Simplify:
3(c-2d)-2(2c-3d)
3(c-2d)-2(2d-3d)
3(c)+3(-2d)-2(2c)-2(-3d)
3c-6d-4c+6d
-c
Simplify:
5(2z-6a)=5(2+z)+a
5(2z-6a)=5(2+z)+a
5(2z)+5(-6a)=5(2)+5(z)+a
10z-30a=10+5z+a
-10z+30a -10z+30a
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+6, -1+5)
(3,4)
Evaluate:
z(b-a) + 2(ab) if z=3, b=2, and a=-5
(3)(2) + (3)(-5) + (2)(-5)(2)
6 + -15 + -20
-29
Simplfiy:
2m^2(5m^3-2m+1)
2m^2(5m^3-2m+1)
2m^2(5m^3)+2m^2(-2m)+2m^2(1)
10m^5-4m^3+2m^2
Simplify:
-4.1 - 5x^2 - 8.6x + 3.05x + 8.1y^2 - 21.4x^2 + 3.2
-4.1-5x^2 - 8.6x + 3.05x + 8.1y^2 - 21.4x^2 +3.2
-0.9 - 5x^2 - 8.6x + 3.05x + 8.1y^2 - 21.4x^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'?
(8-4, -2+12)
(4,10)
Evaluate:
ab(f - 3)(z) if a=3, b=5, f=-2, and z=2.
(3)(5)(f - 3)(z)
15(-2)(2) + 15(-3)(2)
-60 - 90
-150