Title: Section 6'3 Special Products
1Section 6.3Special Products
- Math 65 Blitzer 3rd Edition
2 6.3 Special Products Objectives (p343)
- Use FOIL in polynomial multiplication.
- Multiply the sum and difference of 2 terms.
- Find the square of a binomial sum.
- Find the square of a binomial. difference.
3 6.3 Obj 1 The Product of Two Binomials
FOIL-p343
- Since we are often finding the product of 2
binomials, we look for a Quick Way to get it done
and to help us minimize errors. - Multiply the First terms in the binomial,
- Then the Outside terms
- Then the Inside terms
- Then the Last terms
- It really is just Distribute the 1st term
- Then distribute the 2nd term in disguise.
4Multiplying Polynomials Special Binomial Products
5Multiplying Polynomials Special Binomial Products
6 6.3 Obj 1 The Product of Two Binomials
FOIL-p344
Using the FOIL Method to Multiply Binomials
(ax b)(cx d) a xcx axd bcx bd
First Outers Inners
Last Then combine any like terms
O
F
76.3 Obj 2 Multiply the Sum and Difference of
Two Terms-p345
Consider the two terms 4y and 3 Write the Sum of
these terms Write the Difference of these
terms Multiply the Sum and Difference of these
terms using FOIL (or FLIO or box or vertical
format) Whats a fast way to get the answer?
86.3 Obj 2 Multiply the Sum and Difference of
Two Terms-p345
Try again-lets see if it works Write the sum
and the difference of 5x and 7. What should the
product be? Use FOIL, or any other method to
check. What happens to the middle term? Why?
(Keep this in mind when we have to go the other
way!
96.3 Obj 2 Multiply the Sum and Difference of
Two Terms-p345
- The Product of the Sum and Difference of Two
Terms - (A B)(A B)
- In wordsThe product of the sum and the
difference of the same two terms is
Now try p349 30,34,36,40
106.3 Obj 3 Find the Square of a Binomial
Sum-p346-7
- The Square of a Binomial Sum
- (A B)2 (A B) (A B)
- In wordsThe square of a binomial sum is First
term squared, plus two time the product of the
terms plus the last term squared.
Now try p349 48
116.3 Obj 4 Find the Square of a Binomial
Difference-p346-7
- The Square of a Binomial Difference
- (A - B) 2 (A - B) (A - B)
- In wordsThe square of a binomial difference is
First term squared, minus two time the product of
the terms plus the last term squared.
Now try p349 58
12Area of a Square with Side Length (A B)
(A B )2 (A B ) (A B ) F O I
L A1 A2 A3 A4 A2 AB AB B2
A2 2AB B2
13FOIL and Special Products, Summary See p348 for
examples too!
The Square of a Binomial Sum (x y)2 x 2
2xy y 2 The Square of a Binomial Difference (x
- y)2 x 2 - 2xy y 2 Product of a Sum
Difference of Two Terms (x y) (x - y) x 2 -
y 2 FOIL - General Form (a b) (c d) ac ad
bc bd
14Problem Solving
The square painting shown is surrounded by a
frame that uniformly measures 1 inch wide. If
the frame area is 28 in2, find the dimensions of
the painting.
15Math 65 too fast?
- Consider Math 62-started with Chapter 4, meets 4
days per week, 1 hour at a time. Then take Math
63 in the spring. - Would not have to take Math 65
- Math 61, 62, 63 is the same as 60, 65
- Take Math 65, 3 ,4 or 5 days per week instead of
only 2 days. - Self-paced courses-Math Center
16On a sheet of paper for one Quiz point Print your
name and
From TODAYS lesson 1) Describe one main math
idea 2) Identify one math concept or idea that
interests you. 3) Ask at least one question
about the math we covered.