#### 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. \(\frac{{ac}}{{bc}} = \frac{a}{b}\).

#### Simplifying radical expressions

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.

#### Second-degree polynomial equations

See quadratic equations.

#### 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.