Property
Allows you to "move" parenthesis
(2+3)+7=2+(3+7)
Associative Prop.
What is the GCF of 12yx3 and 18xy5
6xy
Factor 16+20
4(4+5)
Are the expressions 3(x+2)=3x+6 equal?
Yes
What does G.C.F. stand for?
What is Greatest Common Factor.
Does not matter if you "Switch" numbers around
a+b=b+a
Commutative Prop.
GCF of 24a2b3c and 144ab3c2
12ab3c
Factor 3x2+12x
3x(x+4)
Are the expressions 2(x+3)+4 and 2x+8 equal?
No. Simplifying 2(x+3)+4 gives 2x+6+4=2x+10, while 2x+8 remains 2x+8. Therefore, 2x+10≠2x+8
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The process of "reversing" the distributive property
Factoring
GCF of 42, 56, and 70
14
Factor 8xy2+16y
8y(xy+2)
Are the expressions (x+4)(x−2) and x2+2x−6 equal?
No. Expanding (x+4)(x−2) gives
x2-2x+4x-8 = x2+2x-8, while x2+2x-6 is already simplified.
This animal is a distant relative of the dinosaur
What is the Chicken
This property allows multiplication to carry over addition
Distributive Prop.
GCF of 48 and 64
16
2x4-32x2+2x
2x(x3-16x+1)
Are the expressions 5(x+2) and 5x+15 equal?
No. Simplifying 5(x+2) gives 5x+10, while the second expression is 5x+15. Therefore, 5x+10≠5x+15.
This force is why objects fall to the ground when dropped.
What is gravitational force?
This operations "breaks down" under all of the properties
Subtraction
GCF of 60, 75, and 90
15
Given this Factor,
9xy3+27x2y
what is my GCF
9xy
Are the expressions (2x+3)(x−4) and x2−8x+3x−12 equal?
No. Expanding (2x+3)(x−4) gives: 2x(x−4)+3(x−4)=
2x2−8x+3x−12=
2x2−5x−12=
2x(x - 4) + 3(x - 4) =
2x2 - 8x + 3x - 12 =
2x2 -5x-12=
2x(x−4)+3(x−4)=
2x2−8x+3x−12=
2x2−5x−12.
The ocean on the east coast of the United States.
What is the Atlantic Ocean?