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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.
\[{a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0}\]

 
Glossary: S

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