# ABCDEFGHIJKLMNOPQRSTUVWXYZ

#### System of linear inequalities

A set of two or more inequalities.

#### System of linear equations

A set of two or more equations.

#### Sum of difference of two cubes

Let $a$ and $b$ be real numbers, variables, or algebraic expressions.
1. $${\rm{ }}{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} – ab + {b^2}} \right)$$ 2. $${\rm{ }}{a^3} – {b^3} = \left( {a – b} \right)\left( {{a^2} + ab + {b^2}} \right)$$

#### Sum and difference of two terms

Let $a$ and $b$ be real numbers, variables, or algebraic expressions.
$$\left( {a + b} \right)\left( {a – b} \right) = {a^2} – {b^2}$$

#### Sum

The result when two or more numbers are added.

#### Subtracting one integer from another

Add the opposite of the integer being subtracted to the other integer.

#### Subtracting fractions with unlike denominators

Rewrite the fractions so that they have like denominators. Then use the rule for subtracting fractions with like denominators.

#### Subtracting fractions with like denominators

Let $a$, $b$, and $c$ be integers with $c$$$\ne$$0. Then use the following rule: $$\frac{a}{c} – \frac{b}{c} = \frac{{a – b}}{c}$$.

#### Subtraction property of inequalities

Subtract the same quantity form each side. If $$a < b$$ , then $$a + c < b + c$$.

#### Standard form of a polynomial

Let $${a_n},{\rm{ }}{a_{n – 1}},{\rm{ }}…,{\rm{ }}{a_2},{\rm{ }}{a_1},{\rm{ }}{a_0}$$ be real numbers and let n be a non negative number. Order the terms with descending exponents.

${a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0}$

#### Standard form of an equation in one variable

Let $${a_n},{\rm{ }}{a_{n – 1}},{\rm{ }}…,{\rm{ }}{a_2},{\rm{ }}{a_1},{\rm{ }}{a_0}$$ be real numbers and let n be a nonnegative number. Order the terms with descending exponents.

${a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0} = 0$

#### Standard form of a complex number

Let $a$ and $b$ be real numbers. $$a + bi$$

#### Squaring property of equality

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. If $a = b$, then it follows that $a^2 = b^2$.

#### Square root property (complex square roots)

The equation $${u^2} = d,{\rm{ }}d < 0$$, has exactly two solutions: $$u = \sqrt {\left| d \right|} i$$ and $$u = - \sqrt {\left| d \right|} i$$. These solutions can also be written as $$u = \pm \sqrt {\left| d \right|} i$$.

#### Square root property

Let $u$ be a real number, a variable, or an algebraic expression, and let $d$ be a positive real number; then the equation $u^2 = d$ has exactly two solutions.
If $u^2 = d$, then $$u = \sqrt d$$ and $$u = – \sqrt d$$. These solutions can also be written as $$u = \pm \sqrt d$$.

#### Square root of x squared

If $x$ is a real number, then $$\sqrt {{x^2}} = \left| x \right|$$. For a special case in which you know that $x$ is a non-negative real number, you can write $$\sqrt {{x^2}} = x$$.

#### Square root

When $n = 2$ in $$a = {b^n}$$.

#### Square of a binomial

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. $${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$$ $${\left( {a – b} \right)^2} = {a^2} – 2ab + {b^2}$$

#### Solve an inequality

Finding all values of the variable(s) for which an inequality set is true.

#### Solve

Find all values of the variable(s) for which the equation is true.

#### Solutions

The values of the variable(s) for which an equation is true.

#### Solution set

The set of all real numbers that are solutions of an inequality.

#### Slope-intercept form

The form of the equation $$y = mx + b$$ where the slope of the line is $m$ and the $y$-intercept is $$\left( {0,b} \right)$$.

#### Slope

The change in $y$ divided by the change in $x$ of two points.

#### Simplifying rational expressions

Let $a$, $b$, and $c$ represent real numbers, variables, or algebraic expressions such that $$b \ne 0$$ and $$c \ne 0$$. Then the following is valid. $$\frac{{ac}}{{bc}} = \frac{a}{b}$$.

A radical expression is said to be in simplest form when all three of the following statements are true. 1. All possible $n$th-powered factors have been removed from each radical. 2. No radical contains a fraction. 3. No denominator of a fraction contains a radical.

#### Simplify an algebraic expression

Remove symbols of grouping and combine like terms.

#### Scientific notation

Writing a number, usually very large or very small, in the form $$c \times {10^n}$$, where $$1 \le c < 10$$ and $n$ is an integer.

#### Satisfy

The solutions of an equation are said to satisfy the equation when the equation yields a true statement.

Glossary: S