Equations and Inequalities

Rules for Equality: For all real numbers a, b, and c, if a = b, then the following rules are valid.

$${\rm{a + c = b + c}}$$ $${\rm{a - c = b - c}}$$ $${\rm{a*c = b*c}}$$ $${a \over c}{\rm{ = }}{b \over...

Polynomials

A polynomial is an expression involving constants, variables with natural number exponents, the four basic operations of +, -, . and / and no variables in denominators.

Rules for Addition and Subtraction of Polynomials

1. Two terms cannot be added (or subtracted) unless they consist of the...

Order of Operations

• When evaluating mathematical expressions we follow this order of operations:

1. Parentheses (from the inside out)
2. Exponents (from right to left)
3. Multiplication and division (from left to right)
4. Addition and subtraction (from left to right)

Example:

Evaluate the expression: $$\eqalign{ & {{2 \times...

Exponents

• Rules of Exponentiation: For real numbers a and b and natural numbers m and n:

$${{\rm{a}}^{\rm{m}}} \times {\rm{ }}{{\rm{a}}^{\rm{n}}}{\rm{ = }}{{\rm{a}}^{{\rm{m + n}}}}$$

$${{{a^m}} \over {{a^n}}} = {a^{m - n}}$$

$${\left( {{a^m}} \right)^n} = {a^{mn}}$$

$${\left( {ab} \right)^n} = {a^n}{b^n}$$

$${\left( {{a \over b}} \right)^n} = {{{a^n}} \over {{b^n}}}$$

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