Download 3x + 4y - 4

The Distributive Property & Expressions
Tool Box:
Distributive Property
Subtraction Rule
Summary:
Question:
Terms and Coefficients:
term
term
3x + 4y
variable
coefficient
term
-
4 -
variable constant
coefficient
term
6x
term
+ 2
variable constant
coefficient
Identify the Parts of An Expression:
3x + 4y
-
4 - 6x + 2
Parts of an expression separated
by + or (-)
Terms that have the same variable
and exponent
3𝑥𝑦 5 11𝑥𝑦 5
The number in front of the
variable
A number that does not have a
variable
Terms:
3x, 4y, (-4), (-6x), 2
Like Terms:
3x and (-6x)
(-4) and 2
Coefficients: 3, 4, (-6)
Constant:
(-4) and 2
YOU Try It!
2y – 5 + 8x – 3 - 4y
Identify the parts of the
expression
Terms:
Like Terms:
Coefficients:
Constant:
Distributive Property:
Example 1
Algebraically
Numerically
𝒂(𝒃 + 𝒄)
𝒂(𝒃) + 𝒂(𝒄) *
ab + ac
𝟒(𝟐 + 𝟑)
𝟒(𝟐) + 𝟒(𝟑) *
8
+ 12
20
Distributive Prop. Over
Addition
1. Write the Expression
2. Distribute the number (factor)
outside the parentheses to ALL of
the numbers/variables inside the
parentheses
*Creates equivalent expressions
3.Simplify
Example 2:
Algebraically
Numerically
𝒂(𝒃 − 𝒄)
𝟒(𝟐 − 𝟑)
a(b) - a(c)
4(2) - 4(3)
ab - ac
8 - 12
Distributive Prop over
Subtraction
1. Write the Expression
2. Distribute the number (factor)
outside the parentheses to ALL
the numbers/variables
inside the parentheses
3. Simplify
(-4)
Example 3:
Algebraically
(𝒃 + 𝒄)𝒂
(b)a + (c)a
ab + ac
Example 4:
Algebraically
(𝒃 − 𝒄)𝒂
Numerically
(𝟐 + 𝟑)𝟒
(2)4 + (3)4
8
+ 12
20
Numerically
(𝟐 − 𝟑)𝟒
(b)a - (c)a
(2)4 - (3)4
ab
8 - 12
-4
- ac
Try It!
(𝒂 + 𝟓)𝟔
(𝟒 − 𝒙)𝒙
Example 5:
Algebraically
Numerically
−𝟑(𝟕 + 𝒙)
𝟏𝟔 𝒕 − 𝟐(𝒕 − 𝟒)
16t + -2(t + -4)
1. Write the Expression
2. Distribute the number (factor)
outside the parentheses to ALL of
the numbers/variables inside the
parentheses
3. Simplify
1. Write the Expression
2. Distribute the number (factor)
outside the parentheses to ALL of
the numbers/variables inside the
parentheses
3. Simplify
1. Write the Expression
2. Distribute the number (factor)
outside the parentheses to ALL of
the numbers/variables inside the
parentheses
Simplify
Distribute a Negative
Number
1. Write the Expression
2. Subtraction Property (change
the subtraction sign to an addition
sign, then change the term that
follows to its opposite sign
-3(7) + -3(x)
16t + -2(t) + -2(-4)
-21 + -3x
16t + -2t + 8
14t + 8
-3x – 21
14t + 8
Example 6:
Find the perimeter and area of the rectangle
2. Distribute the number (factor)
outside the parentheses to ALL of
the numbers/variables inside the
parentheses
3. Simplify
4. Combine Like Terms
*Watch your
Signs/Symbols/Operations
3. Rewrite your expression so that
it is in order. Constant is last
Geometry:
9
8 – 12w
9+ 9 + 8 -12w + 8 -12w
-12w – 12w + 9 + 9 + 8 + 8
-24w + 34
A = bh
A = (8 - 12w) 9
A = (8 + -12w) 9
A = 9 (8) + 9 (-12w)
A = 72 – 108w
A = -108w + 72
Try It! Simplify:
1.
𝟔𝒚 − 𝒚
(𝟒𝒂 − 𝟏)𝟐 + 𝒂
2.
3. 𝟑(𝒎 + 𝟓) − 𝟏𝟎
4. (𝒔 − 𝟑)(−𝟐) + 𝟏𝟕𝒔
5. Find the perimeter and area of the rectangle:
5
v+3
Perimeter:
1. Write the expression for the
perimeter of the shape
2. Combine like terms using the
commutative property
3. Simplify
Area:
1.Write the area formula
2. Substitution Property
3. Subtraction Property
4. Distributive Property
5. Simplify