Outro W7

6.1 Add and Subtract Polynomials

• Monomials
  • A monomial is a term of the form $ax^m$, where a$a$ is a constant and m$m$ 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
    Product Property                    \(a^m\cdot a^n=a^{m+n}\)

           Power Property                      \(\left(a^m\right)^n=a^{m+n}\)

           Product to a Power                \(\left(ab\right)^m=a^m\cdot a^n\)

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 Links to an external site.)
  • FOIL Method (Example 6.39 Links to an external site.)
  • Vertical Method (Example 6.44 Links to an external site.)
    

• Multiplying a Trinomial by a Binomial—To multiply a trinomial by a binomial, use the:
  • Distributive Property (Example 6.45 Links to an external site.)
  • Vertical Method (Example 6.46 Links to an external site.)

6.4 Special Products

• Binomial Squares Pattern
  • If a,b$a,b$ are real numbers,
    
  • $\left(a+b\right)^2=a^2+2ab+b^2$
  • $\left(a-b\right)^2=a^2-2ab+b^2$
  • To square a binomial: square the first term, square the last term, double their product.
    
    
• Product of Conjugates Pattern
  • If a,b$a,b$ are real numbers,
    
  • $\left(a-b\right)\left(a+b\right)=a^2-b^2$
  • 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