Translating algebraic expressions 1
The square of the sum of a number and 5
(n+5)^2
10 minus a number
10 - x
a number subtracted from ten
10 - x
Ten thousand times the sum of a number and seven hundred
10000(x + 700)
ten times a number
10x
the product of 10 and a number
10x
Eighteen more than the square root of a number
18+√n
A number subtracted from 18
18-n
The quotient of 18 and a number
18/x
Two times a number and its cube
2(n+n^3)
Six less than double a number
2n-6
double a number
2x
Five more than twice a number
2x + 5
Five less than twice a number.
2x - 5
Three times the difference of a number and seven.
3(x - 7)
three times the sum of a number and 2
3(x+2)
Three-fourths of a number decreased by eight.
3/4x - 8
Thirty divided by a number
30/n
The product of a number and three
3x
triple a number
3x
Three times a number, increased by seventeen
3x + 17
The product of a number and three plus seven.
3x + 7
Eleven less than three times a number
3x - 11
Nine less than the product of a number and four
4x - 9
5 increased by four times a number
5+4x
Seven more than the quotient of ten and a number.
7 + 10/n
Seven divided by the sum of a number and two.
7/(x + 2)
The product of nine and a number decreased by six.
9x - 6
Constant
A number that doesn't change. There is no variable attached to a constant.
Factor (as a noun)
A number that is multiplied by another number to get a product
Variable
A symbol used to represent an unknown amount. The symbol is usually a letter of the alphabet.
Factored Form
An expression in factored form has the GCF on the outside of the parentheses, and a sum or difference on the inside.
Algebraic Expression
An expression that contains variables.
SPECIAL NOTE!!!!!!
Any variable with no coefficient has "AN INVISIBLE 1" attached to it x = (1) x
Terms
Quantities that you ADD to form an Algebraic expression are called terms
Combining Like Terms
Search for like terms (SAME VARIABLE raised to the SAME POWER; and CONSTANTS with other CONSTANTS
Unlike Terms
Terms whose variables ARE NOT the same, or who have the SAME variable, but it's raised to a DIFFERENT power
Like Terms
Terms with SAME variable raised to the SAME power. You CAN add / subtract like terms
Distributive Property
The distributive property combines multiplication with addition and subtraction
Greatest Common Factor
The largest factors that is shared by two or more numbers
Coefficient
The number being multiplied by a variable. It is the number ATTACHED to the variable, and is usually in front.
Factor (as a verb)
When you factor an expression, you reverse the distributive property. The number on the outside of the parentheses is the GCF.
the sum of h and 15
h+15
The sum of a number and its square
n + n^2
A number added to 10
n+10
Ten added to a number
n+10
Thirty-six subtracted from a number
n-36
A number minus the cube of four
n-4^3
A number divided by 11
n/11
A number squared
n^2
Five added to the cube of a number
n^3 +5
Sixteen subtracted from a number cubed
n^3-16
17 less than w
w-17
a number increased by 10
x + 10
ten more than a number
x + 10
three more than a number
x + 3
10 less than a number
x - 10
a number decreased by 10
x - 10
the difference of a number and ten
x - 10
The difference between a number and seven.
x - 7
twenty seven more than a number
x+27
a number divided by 2
x/2 or x÷2
one third of a number
x/3 or (1/3)x
a number divided into 6 parts
x/6
a number times itself
x²
one fourth of a number
¼x or x/4