Transcript d) Combine Terms & Properties Review

Review Day!
copyright©amberpasillas2010
a(b  c)  a  b  a  c
or
a(b  c)  a  b  a  c
copyright©amberpasillas2010
I am going to show you 2 ways to solve this expression.
3(4  5)
Order of Operations
3(4  5)
3(9)
27
Distributive Property
3(4  5)
3(4) 3(5)
12  15
27
Let’s see if it works the same way for subtraction!
copyright©amberpasillas2010
I am going to show you 2 ways to solve this expression.
5(10  3)
Order of Operations
5(10  3)
5(7)
35
Distributive Property
copyright©amberpasillas2010
5(10  3)
5(10) 5(3)
50  15
35
So you are probably thinking why use the Distributive
Property when Order of Operations is easier? Just watch!
Order of Operations
4(x  2)
Distributive Property
You can’t add x + 2 because
they are different terms!
4(x  2)
4(x) 4(2)
4x  8
Why use the Distributive Property?
It helps you simplify when letters are used!
copyright©amberpasillas2010
The Distributive Property helps with mental math!
4 • 83
4(80 + 3)
80 + 3
4 4(80)
+ 4(3)
= 320 + 12
= 332
x + 4
5(x + 4)
5
5(x)+ 5(4) = 5x + 20
copyright©amberpasillas2010
Use the distributive property to simplify.
1) 2(x + 8)
2) 3(a - 8)
2x + 16
3a - 24
3) -7(8 - m)
4) 4(5- a)
-56 + 7m
20 - 4a
5) (10 - k)5
6) x(y + z)
xy + xz
50 - 5k
Identity Property of Addition
a0a
Identity remains the same
Zero is called the additive identity
Identity Property of Multiplication
a 1  a
Identity remains the same
One is called the multiplicative identity
copyright©amberpasillas2010
Name the property shown below.
1) (6 + 3) + 1 = (3 + 6) + 1
Commutative Property of Addition
Order doesn’t matter
Flip-Flop
2) 10  (8  3)  (10  8)  3
Associative Property of Multiplication
Re-Grouping
copyright©amberpasillas2010
Terms: Numbers and/or variables tied together
by multiplication or division but
separated by addition or subtraction.
How many terms? 6 terms
6x
7x  3y  4abc  2  k  2
m
copyright©amberpasillas2010
Coefficient: The number preceding the
variable in a variable term.
How many coefficients? 5 coefficients
6x
7x  3y  4abc  2 1k  2
m
The number IN FRONT OF THE VARIABLE
copyright©amberpasillas2010
Constant: The numerical terms.
(NUMBERS ONLY)
How many constants?
1 constant
6x
7x  3y  4abc  2 1k  2
m
The numbers WITH NO VARIABLES!
copyright©amberpasillas2010
You can use what you have
learned about properties
when combining like
terms.
copyright©amberpasillas2010
Simplify each expression by using the Distributive
Property and combining like terms.
1) 7(x + 4) + 2x
7x + 28 + 2x
2) 5x + 3(x + 1)
5x + 3x + 3
8x + 3
9x + 28
copyright©amberpasillas2010
Simplify each expression by using the Distributive
Property and combining like terms.
3) a + 2(4 + a ) - 1
a + 8 + 2a - 1
4) 3(b - 2) + 6b
3b - 6 + 6b
3a + 7
9b - 6
copyright©amberpasillas2010
Take Out Your Study Guide!!!
copyright©amberpasillas2010
#7
Coefficient: The number in front of the variable.
5 Coefficients
Ex: 3x
-2y 1 m
7x
y
2
2 2
m
3
Terms: The numbers and variables separated
by addition & subtraction.
Ex: 3x + 2y – 8
3 Terms
Constant: The numerical terms.
Ex: 5x + 9 – 6
2 Constants
copyright©amberpasillas2010
Like Terms and Unlike Terms
#8
Terms in an expression are like terms
if they have identical variable parts.
Like Terms
3  5
 8
10x  -2x  8x
2
1 x  8x  9x
2
2
copyright©amberpasillas2010
Unlike Terms
3
x
10x
-2x
2
3
x
8x
2