Revie of the week

You can find the key concepts you studied this week in the following short reviews

6.1
6.2
6.3
6.4

6.1 Add and Subtract Polynomials

Monomials
- A monomial is a term of the form , where $a$ is a constant and $m$ is a whole number
Polynomials
- polynomial—A monomial, or two or more monomials combined by addition or subtraction is a polynomial.
- monomial—A polynomial with exactly one term is called a monomial.
- binomial—A polynomial with exactly two terms is called a binomial.
- trinomial—A polynomial with exactly three terms is called a trinomial.
Degree of a Polynomial
- The degree of a term is the sum of the exponents of its variables.
- The degree of a constant is 0.
- The degree of a polynomial is the highest degree of all its terms.

6.2 Use Multiplication Properties of Exponents

Exponential Notation
Properties of Exponents
- If $a, b$ are real numbers and $m, n$ are whole numbers, then
  $\begin{matrix} Product Property & a^{m} \cdot a^{n} & = & a^{m + n} \\ Power Property & {(a^{m})}^{n} & = & a^{m \cdot n} \\ Product to a Power & {(a b)}^{m} & = & a^{m} b^{m} \end{matrix}$

$\begin{matrix} Product Property & a^{m} \cdot a^{n} & = & a^{m + n} \\ Power Property & {(a^{m})}^{n} & = & a^{m \cdot n} \\ Product to a Power & {(a b)}^{m} & = & a^{m} b^{m} \end{matrix}$

$\begin{matrix} Product Property & a^{m} \cdot a^{n} & = & a^{m + n} \\ Power Property & {(a^{m})}^{n} & = & a^{m \cdot n} \\ Product to a Power & {(a b)}^{m} & = & a^{m} b^{m} \end{matrix}$

6.3 Multiply Polynomials

FOIL Method for Multiplying Two Binomials—To multiply two binomials:
1. Step 1. Multiply the First terms.
2. Step 2. Multiply the Outer terms.
3. Step 3. Multiply the Inner terms.
4. Step 4. Multiply the Last terms.
Multiplying Two Binomials—To multiply binomials, use the:
- Distributive Property (Example 6.34)
- FOIL Method (Example 6.39)
- Vertical Method (Example 6.44)

Multiplying a Trinomial by a Binomial—To multiply a trinomial by a binomial, use the:
- Distributive Property (Example 6.45)
- Vertical Method (Example 6.46)

6.4 Special Products

Binomial Squares Pattern
- If $a, b$ are real numbers,
- $LaTeX: \left(a+b\right)^2=a^2+2ab+b^2$
- $LaTeX: \left(a-b\right)^2=a^2-2ab+b^2$
- To square a binomial: square the first term, square the last term, double their product.
Product of Conjugates Pattern
- If $a, b$ are real numbers,
- $LaTeX: \left(a-b\right)\left(a+b\right)=a^2-b^2$
- The product is called a difference of squares.
To multiply conjugates:
- square the first term square the last term write it as a difference of squares

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