Algebra, Equations, and Inequalities

Question 1

Algebra

Answer 1

The part of math that involves variables

Question 2

Variable

Answer 2

A letter that represents either a specific number OR all numbers

In an expression, we’re trying to find patterns that are true for all numbers

In an equation, we’re trying to solve for a specific number

Question 3

Constant

Answer 3

A number or symbol (like π) that doesn’t change in value

Ex:
5

x

6y^2

Question 4

Term

Answer 4

A product of constants and variables, including powers of variables

Question 5

Coefficient

Answer 5

The constant factor of a term

Note: when no coefficient is listed, the coefficient = 1

Ex: 6y^2 (coefficient is 6)

x^5 (coefficient is 1)

Question 6

Expression

Answer 6

A collection of one or more terms joined by addition and subtraction

Ex:

x + y

Y^2 - x^2

Notice that expressions DONT have equal signs

Question 7

Monomial

Answer 7

An expression with exactly one term

Ex: 5x^2

Question 8

Trinomial

Answer 8

An expression with exactly 3 terms

X^2 - 2x + 3

Question 9

Binomial

Answer 9

An expression with exactly two terms

X^2 + 4x

Question 10

Polynomial

Answer 10

An expression with any number of terms involving one single variable

Question 11

Linear

Answer 11

A term with a single power of a variable (ie: not explicitly written with an exponent)

Question 12

Quadratic

Answer 12

A term with a square of a single variable

X^2 + 4x + 2

Question 13

Cubic

Answer 13

A term with a cube of a single variable

X^3 + 2x^2 + 2

Question 14

Linear Expression

Answer 14

The highest power of the variables is 1

• 17x is a linear monomial
• 3x - 5 is a linear binomial

-Notice, a linear binomial has one linear term and one constant term

Question 15

Quadratic Expression

Answer 15

The highest power of the variable is 2

• 14x^2 is a quadratic monomial
• x^2 - 4 is a quadratic binomial (with one quadratic term and one constant term)
• x^2 + 8x is a quadratic binomial (with one quadratic term and one linear term)
• x^2 + x - 1 is a quadratic trinomial (with one quadratic term, one linear term, and one constant term)

Question 16

Like Terms

Answer 16

1 algebraic simplification rule: we can combine like terms by addition or subtraction!

Any two terms with the same variable part. It they differ at all, they differ in coefficients.

We can only add or subtract like terms NOT terms with different variables or powers.

Notice also that multiplication is commutative, that is, the order of factors in multiplication doesn’t matter.
-5xy and 7yx are still like terms!

Question 17

Adding an algebraic expression involving parentheses

Answer 17

We can simply remove the parentheses and combine like terms

X^3 - 3x^2 + 3x) + (x^3 + 3x^2 -3x
= 2x^3

Question 18

Subtracting algebraic expressions involving parentheses

Answer 18

When a subtraction occurs in front of parentheses, we must first chance every sign inside the parentheses to it’s opposite (addition becomes subtraction and vice versa) and then combine like terms

(-3x^2 + 3x) - (3x^2 - 3x)

= -6x^2 + 6x

Question 19

Square of a sum formula

Answer 19

(a + b)^2

Can find using FOIL

(a + b)(a + b) =

a^2 + ab + ba + b^2 =

a^2 + 2ab + b^2

Question 20

Square of a difference formula

Answer 20

(a - b)^2

Can be found using FOIL

(a-b)(a-b) =

a^2 -ab - ba + b^ 2 =

a^2 -2ab + b^2

Question 21

Distributive Law

Answer 21

P(Q + R) =

PQ + PR

Question 22

Difference of Two Squares

Answer 22

(a+b)(a-b) =

a^2 + ab - ab + b^2 =

a^2 - b^2