Algebra

What are like terms?

Terms that contain the same variables , and the corresponding variables have the same exponents

a^2-b^2 =

(a+b)(a-b)

What is a variable?

A letter that represents a quantity whose value is unknown. Letters x and y are often used as variables, although any symbol can be used.

What is a quadratic equation?

An equation where the variable x is an equation that can be written in the from ax^2 + bx + c= 0

Two equations that have the same solutions are called ______. Give an example.

Equivalent equations x+1 =2 and 2x+4 = 4. Both are true when x=1.

What does an algebraic expression have?

It has one or more variables and can be written as a single term or as a sum of terms.

How do you solve an equation?

You must find the values of the variables that make the equation true, that is, the values that satisfy the equation.

What is equation?

a statement of equality between two mathmetical expressions.

If X^A=X^B then

a=b

(a+b)^2 =

a^2 + 2ab + b^2

(a-b)^2

a^2 - 2ab + b^2

(a+b)^3 =

a^3 + 3a^2b + 3ab^2 + b^3

What is a linear equation?

an equation involving one or more variables in which each term in the equation is either a constant term or a variable multiplied by a coefficient. None of the variables are multiplied together or raised to a power greater than 1. For example, 2x+1=7x and 10x-9y-z=3 are linear equations, but x+y^2=0 and xz=3

How do you write a linear equation with two variables?

ax+by=c

ca +cb=

c(a+b)

ca-cb=

c(a-b)

A number that is multiplied by variables is called the _____ of a term

coeffient

A term that has no variable is called a _______

constant

What is the general method to solving equivalent solutions

find successviley simpler equations so that equivalent equations make the solutions easier. Rule 1: When the same constant is added to or subtracted from both sides of an equation, the equality is presevered and the new equation is equivalent to the original equation. Rule 2: When both sides of an equation are multiplied or divided by the same nonzero constant, the equality is preserve and the new equation is equivalent to the original equation. Rule 3: When an expression that occurs in an equation is replaced by an equivalent expression, the equality is preserved and the new equation is equivalent to the original equation Example: Since the expression 2(x+1) is equivalent to the expression 2x+2, when the expression 2(x+1) occurs in equation, it can be replaced by expression 2x+2, and the new equation will be equivalent to the original equation.

A statement of equality between two algebraic expressions that is true for all possible values of the variables involved is called an ______

identity

If an equation involves one or more variables, the values of the variable that make the equation true are called _____

solutions

What is a degree of a polynomial?

the greatest degree of any term in the polynomial

What is a polynomial?

the sume of a finite number of terms in which each term is either a constant term or a product of a coefficient and one or more variables with positive integer exponents.