Addition of Polynomials
(4x2 + 2x) + (x2 + 6x)
5x2 +8x
(y2 - 10xy) - (2y2 + 3xy)
-y2 -13xy
(6x2)(5x)
30x3
Which property allows you to change where the parentheses are?
Associative Property
(3x2 + 4x -1) + (x2 - 2x + 8)
4x2 + 2x + 7
(-3y2 + y) + (4y2 + 6y)
y2 +7y
(2x2 + 5x - 3) - (3x3 + 2x - 5)
-3x3 + 2x2 +3x + 2
2x(x + 6)
2x2 + 12x
Which property allows you to change the order?
Communative Property
(5x2 + 6x + 13) - (2x2 + 8 )
3x2 + 6x + 5
(2a2 - 7a + 10) + (a2 + 4a + 7)
3a2 -3a +17
(-3a2 - 2a) - (4a2 - 4)
-7a2 - 2a + 4
(4m + 2)(4m + 5)
16m2 + 28m + 10
Simplify the expression using the distributive property:
2(x2 - 4x + 7)
2x2 - 8x + 14
Are the following two expressions equivalent? How do you know?
Expression 1: (3x + 7) - (6x + 4)
Expression 2: -3x + 3
These are equivalent by the associative property of addition.
(2r2 - 5r + 7) + (3r3 - 6r)
3r3 + 2r2 -11r + 7
(4x3 + 5x + 2) - (1 + 2x - 3x2)
4x3 + 3x2 +3x + 1
(a + 3)(a − 2)
a2 + 1a − 6
Are the following two expressions equivalent? How do you know?
Expression 1: (x + 2) + (3x + 4)
Expression 2: 4x + 6
These are equivalent by the associative property of addition.
(2x2 + 5)(x - 2)
2x3 - 4x2 + 5x - 10
(5r3 - 6r2 +3r) + (r2 -2r - 3)
5r3 - 5r2 + r - 3
(4 - x - 2x2) - (-2 + 3x - x3)
x3 - 2x2 - 4x + 6
(x - 2)2
x2 - 4x + 4
Are the following two expressions equivalent? How do you know?
Expression 1: 7x + 2 - 3x + 11
Expression 2: x2 + 4x + 13 - x2
Expression 1: 4x + 13
Expression 2: 4x + 13
We know these are equivalent by the commutative property of addition.
Are the following two expressions equivalent? How do you know?
Expression 1: 8x + 2 + x - 7
Expression 2: 4x + 3x - 5 + 2x
Expression 1: 9x - 5
Expression 2: 9x - 5
These two expressions are equivalent by the commutative property of addition.