1. Objective A. To multiply a polynomial by a monomial
Procedure: To multiply a polynomial by a monomial:
Step 1: Multiply the monomial factor in front of the parenthesis by the factors of each term inside the parentheses. Use the Distributive Property and the Rules for multiplying Monomials.
Solution:
Answer:
Your Turn Problem #1

2. Objective B. To multiply two polynomials
Procedure: To multiply a polynomial by a polynomial:
Step 1: Use the distributive property to “distribute” the first term of the first polynomial by each term of the second polynomial.
Step 2: Then distribute the second term of the first polynomial by each term of the second polynomial. Continue this process if the first polynomial has more than two terms.
Step 3: Combine like terms.
Solution:
Answer:
Your Turn Problem #2

3. Solution:
Answer:
Your Turn Problem #3
Multiply
Solution:
Answer:
Your Turn Problem #4

4. Objective C: To multiply two binomials
The FOIL method is a shortcut based upon the Distributive Property when multiplying two binomials.
In multiplying two binomials, make sure all possible multiplication combinations are performed.
Firsts
Outsides
Insides
Lasts
Procedure: The FOIL method
Step 1: “F” Multiply the left terms of each binomial together (firsts).
Step 2 “O” Multiply the left term of the first binomial times the right term of the second binomial (outsides).
Step 3: “I” Multiply the right term of the first binomial times the left term of the second binomial (insides).
Step 4: “L” Multiply the right term of each binomial together (lasts).
Step 5: Combine like terms.

5. Solution:
Answer:
Your Turn Problem #5

6. Objective D: To multiply binomials with special products
There are a couple of kinds of multiplication of two binomial types which are so common that many students memorize the pattern for each. Using these patterns, problems can be simplified directly to save time.
i. Sum and difference of two terms:
Solution:
Answer:
Next Slide
Note: The answer is always the difference between two squares (middle terms cancel).

7. Procedure: To multiply the sum and difference of two terms:
Step 1. Square the first term of either binomial.
Step 2. Square the second term of either binomial.
Step 3. Write the answer as the difference of two squares.
General Statement: (a + b)(a – b) = a² – b²
Answer:
Your Turn Problem #6

8. ii. The square of a binomial
Solution:
Rewrite as a product without using the exponent. Then FOIL.
Answer:
Note: (a + b)² = (a + b)(a + b)
= a² + ab + ba + b²
= a² + 2ab + b²
Procedure: To square a binomial
Step 1. Square the first term.
Step 2. Multiply- two times the first term times the second terms.
Step 3. Square the second term.
Step 4. A trinomial answer will result. General Statement: (a + b)² = a² + 2ab + b²
Therefore, when a binomial is being squared, a trinomial results with the following pattern:

9. Solution:
Square the first:
Two times the first times the second:
Square the second:
Answer:
Your Turn Problem #7

10. iii. The cube of a binomial
Example: Simplify:
Solution:
Rewrite without using the exponent.
Then multiply the last two binomials.
Then multiply the two remaining polynomials and add like terms.
Answer:
To find a pattern for the cube of a binomial, look at the cube of a general binomial.
Procedure: To cube a binomial:
Step 1. Let a = first term of the binomial.
Let b = second term of the binomial.
Step 2. Substitute a and b into the pattern:
Step 3. Simplify and combine like terms

11. Let a = x
Let b = 5
Solution:
Use the pattern:
Answer:
This problem could have been done by writing (x + 5)³ as (x + 5)(x + 5)(x + 5), and then multiplying it all out. Using the pattern does save time and steps. However feel free to choose the method you are most comfortable with.
Your Turn Problem #8

12. Solution: Let a = 2x Let b = –5 Answer: Your Turn Problem #9 The End.
B.R.