Distributive Property
Simplify using distributive property:
4(x+8)
4x+32
Are 4x and 7x2 like terms? Why or why not?
No, they are not like terms. Even though they have the same variable (x), they do NOT have the same power (squared).
VOCAB: What is a letter that stands for an unknown number?
Ex: y in 7y
a variable
X + 8 = 12
What is X = 4
Check
4 + 8 = 12
6y=36
y = 6
Simplify using distributive property:
3(x-7)
3x-21
Are 4 and 3 like terms?
Yes, they are both constant terms. Both terms have no exponent and no power, so they match.
VOCAB: What is a number that is multiplied by a variable?
Ex: 7 in 7y
A Coefficient
90=x+72
x=18
check
90 = 18+72
56=7x
x=8
Check
56=7(8)
Simplify using distributive property:
2(5x+6)
10x+12
Simplify the expression by combining like terms:
7+3x-5+4x
2+7x
or
7x+2
VOCAB: What must two terms have in common to be considered "like terms"?
They must have the same variable and the same power (exponent).
Ex: 5x2 and 32x2
X + 27 = 84
What is x = 57
Check
57 + 27 = 84
12x=60
x=5
Check
12(5)=60
Simplify using distributive property:
7(4x+9)
28x+63
Simplify the expression by combining like terms:
8+9y-4+3y
4+12y
or
12y+4
Haley and Andrea participated in a quiz contest. They scored 23 points in all. Haley scored 9 points. Write an equation to represent how many points Andrea scored.
x+9 =23 or 23=x+9
x+9=12+27
x=30
Check
30+9=12+27
4y=56-32
y=6
Check
4(6) = 56-32
Simplify using distributive property:
(x+3)5
5x+15
Simplify the expression by combining like terms:
4x+6xy-3+6-8y+7xy
4x+13xy-8y+3
Tom has 25 bumblebee marbles and Marcus has a few more than Tom. If they have 56 marbles in all, write an equation for how many bumblebee marbles Marcus has?
Let X = number of Marcus's Bumblebee Marbles
x+25 = 56 or 56 = x+25
213 + X = 471
What is X = 258
Check
213+258 = 471
75=5y
y=15
check
75 = 15 (5)