Adding Polynomials
Simplify the expression
(y + 2) + (y2 + 2y +4)
y2 + 3y +6
Simplify the expression
(y + 2) - (2y +4)
-y -2
Simplify the expression
2(x+10)
2x + 20
This property says that changing the order of addition or multiplication will not change the outcome.
Commutative Property
Simplify the expression:
5 + (9 + 10)4 - 7(5)
46
Simplify the expression:
(a2 + 4a +8) + (a2 -2a -2)
2a2 + 2a + 6
Simplify the expression:
(a2 + 4a +8) - (a2 -2a -2)
6a + 10
Simplify the expression
-x(5 - x)
x2 - 5x
The associative property says you can change the ____________ of numbers by using parenthesis, and it will not change the outcome.
grouping
What do we call two terms that have the same variable and exponent?
Like-terms
Simplify the expression
(6 - 2y + y2) + (4y2 -3y -1)
5y2 - 5y + 5
Simplify the expression
(6 - 2y + y2) - (4y2 -3y -1)
-3y2 + y + 7
Simplify the expression
(x+1)(x+4)
x2 + 5x + 4
The ___________ property proves these are equivalent expressions.
2x + 5(x - 1) = (-1 + x)5 + 2x
Commutative
Solve for x
3x = 18
x=6
Simplify the expression
(2x - 5 + x + x - 5) + (x + 15 + x + 2x + 15)
8x + 20
Simplify the expression
(2x - 5 + x + x - 5) - (x + 15 + x + 2x + 15)
-40
Simplify (w3 -w +1)(w2 +1)
w5 + w2 -w +1
The _____________ property proves these are equivalent expressions.
a + (5 + b) = (a + 5) + b
Associative
What is a possible value for x?
x + 5 > 15
x > 10
(possible answers include 11, 12, 13, 14...)
Simplify the expression:
x3 + 5x +2x2 - 3x + x2 +2x4
2x4 + x3 + 3x2 + 2x
Simplify the expression:
(x3 + 5x +2x2) - (3x + x2 +2x4)
-2x4 + x3 + x2 +2x
Simplify the expression:
(x2 - 3x + 11)(x2 +9)
x4 - 3x3 + 20x2 - 27x + 99
The ____________ property proves these are equivalent expressions.
(2x)y + (1 + y) = (xy)2 + (1 + y)
Associative
Solve the equation
2x + 4 = 12
x=4