Algebraic expressions Flashcards
What are like terms?
Terms that contain the same variable(s) and the variable(s) have the same exponent(s)
What is a constant term?
A term with no variables and only a coefficient.
What is a coefficient of a term?
The number in front of the variable(s). This number is multiplied by the variable(s).
What is a polynomial?
A polynomial is the sum of an algebraic expression with a countable number of terms and positive variable coefficients.
What is the degree of a term?
The sum of the exponents of each of the variables of that term.
What is the degree of a polynomial?
The greatest degree of its terms.
What is a variable?
A letter that represents an unknown quantity.
What is an algebraic expression?
An expression with one or more variables that contains one term or a sum of multiple terms.
What is a term? What is a single term?
A single term is a singe product of variables and coefficients where either the variables or coefficients can be 0.
E.g. x, 3, 3x, and 3x^2 are terms.
How do you add algebraic expressions?
The coefficients of like terms can be added together.
E.g. 3x can be added to 7x to equal 10x. 3x and 4x^2 can not be added together since the exponents of the variables are different.
How do you subtract algebraic expressions?
Like terms can be subtracted by subtracting the coefficients. Terms that are not like cannot be subtracted.
E.g. 2y can be subtracted from 5y to get 3y.
How do you multiply algebraic expressions?
Each term of the first expression is multiplied by each term of the second expression.
How do you divide algebraic expressions?
The common factors can be factored out of the numerator and denominator and the term can then be simplified.
What are the 7 algebraic identities?
- ca+cb = c(a+b)
- ca-cb=c(a-b)
- (a+b)^2=a^2+2ab+b^2
- (a-b)^2=a^2-2ab+b^2
- a^2-b^2=(a+b)(a-b)
- (a+b)^3=a^3+3a^2b+3ab^2+b^3
- (a-b)^3=a^3-3a^2b+3ab^2-b^3
