Expressions & Equations Flashcards
double distribution
distributing terms through two sets of parentheses
known as FOIL when used on two sets of binomials in parentheses
Common difference
The difference between the terms in a sequence.
Order of operations
PEMDAS: the set order in which multi-step equations must be solved: Parenthesis, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)
Distributive property
a number in front of a group of terms will multiply all terms in the grouping individually
factored
Separated into factors or divisors that, when multiplied together, yield the original number.
Dissecting (math)
writing numbers or expressions in expanded form
variable (math)
A letter or non-numeric symbol that represents an unknown value.
ex: In the expression 2x+4y−5, there are 2 variables: x and y.
Multiplication property of equality
If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal.
if a=b, then ac=bc
Addition property of equality
If the quantities on each side of an equal sign have the same amount added to them, the resulting statement will still be equal.
If a=b, then a+c=b+c
Common ratio
The amount you multiply by to get from one term to the next in a sequence
Like term
terms with the same variable and exponent combination
Example: 2x and 5x
System of linear equations
A set of two or more equations with the same set of variables, or unknowns. The solution is the intersection of the lines.
Linear relationship
a relationship with a constant rate of change that creates a straight line when graphed
y=mx+b
shape pattern
A sequence composed of a repeating pattern of shapes
Sequence
a list of numbers, shapes, symbols, or terms listed in a specific order; most follow a pattern
function table
a table that describes a function by displaying inputs and corresponding outputs in a table format
Inequality
A statement that 2 expressions are not equal.
Example: 5>4
Term
Each part of an expression that is separated by a + or - sign.
Example: In the expression 7x+6y−5, there are 3 terms: 7x, 6y, and −5.
Division property of equality
If the quantities on each side of an equal sign are both divided by the same amount, the resulting statement will still be equal.
If a=b and c≠0, then a÷c=b÷c
Expression
Numbers, symbols, and operators grouped together to show the value of something. Note that it differs from an equation because there is no equal sign and therefore cannot be solved, only simplified.
Example: 3x−4y+6
Geometric sequence
A sequence whose terms are generated by multiplying each term by the same common ratio.
Linear expression
An expression that does not contain any exponents
Example: 2x+3
Algebra
The branch of mathematics in which letters and symbols are used to represent unknown values.
arithmetic sequence
A sequence that has the same common difference between terms.
Equation
A statement that two expressions are equal. It has an equal sign and therefore can be solved.
Example: 2x+4=6
Subtraction property of equality
If the quantities on each side of an equal sign have the same amount subtracted from them, the resulting statement will still be equal.
Example: If a=b, then a–c=b–c
constant
a number without a variable; value does not change (stays constant)
Example: In the expression 2x+4y−5, the constant is −5
Coefficient
A number that multiplies a variable.
Example: In the expression 3x+1, 3 is the coefficient of x
Combine like terms
method of simplifying an algebraic expression by adding or subtracting the coefficients of like terms
Example: 2x+4x=6x
Distribution (mathematics)
Use of the distributive property where a number in front of a group of terms will multiply all terms in the grouping individually.
