Transcript 6.9 Some Special Products CORD Math Mrs. Spitz Fall 2006 Objective After studying this lesson, you should be able to use patterns for: – (a +

6.9 Some Special Products
CORD Math
Mrs. Spitz
Fall 2006
Objective
After studying this lesson, you should
be able to use patterns for:
– (a + b)2
– (a – b)2
– (a + b)(a – b)
Assignment
Pg. 245 #4-35 all
Connection
METHOD 1: The
length of each side is 6
+ 2 units. The area is
the product of (6 + 2)
and (6 + 2) of (6 + 2)2.
(6 + 2)2 = 82
= 64
6
2
6
2
Connection
METHOD 2: The area
of the large square is
the sum of the areas of
the four smaller
rectangles.
62 + 6 · 2 + 6 · 2 + 2 2 =
36 + 12 + 12 + 4
= 64
6
2
6
Thus, (6 + 2)2 = 62 + 6 · 2 + 6 · 2 = 22.
2
Connection
Using similar
procedure as the one
described, we can
derive a general form
for the expression (a +
b)2.
6
2
6
2
Square of a Sum
(a + b)2 = (a + b)(a + b) = a2 + 2ab +b2
Ex. 1: Find (x +
2
3)
(x + 3)2 = (x + 3)(x + 3)
= x2 + 2(x)(3) + b2
= x2 + 6x + b2
Ex. 2: Find (5m +
2
3n)
(5m + 3n)2 = (5m + 3n)(5m + 3n)
= (5m)2 + 2(5m)(3n) + (3n)2
= 25m2 + 30mn + 9n2
Square of a Difference
(a - b)2 = (a - b)(a - b) = a2 - 2ab +b2
Ex. 3: Find (c –
2
2)
(c – 2)2 = (c – 2)(c – 2)
= c2 – 2(c)(2) + 22
= c2 – 4c + 4
Ex. 4: Find (3x –
2
2y)
(3x – 2y)2 = (3x – 2y)(3x – 2y)
= (3x)2 – 2(3x)(2y) + (2y)2
= 9x2 – 12xy + 4y2
Note:
You can use the FOIL method to find the
product of a sum and difference of the same
two numbers.
(a + b)(a – b) = (a)(a) +(a)(-b) + (a)(b) + (b)(-b)
= a2 – ab + ab – b2
= a2 – b2
This product is called a difference of squares.
Product of a Sum and a Difference
(a + b)(a – b) = (a – b)(a + b) = a2 – b2
Ex. 5: Find (x + 5)(x – 5)
(x + 5)(x – 5) = x2 – 52
= x2 – 25
Ex. 6: Find (5a + 6b)(5a – 6b)
(5a + 6b)(5a – 6b) = (5a)2 – (6b)2
= 25a2 – 36b2
Reminders
1st period – 6.9 is due on Tuesday after we
return. We will work on Chapter 6 review
on Tuesday. Test on Wednesday.
4th period – 6.9 is due Wednesday after we
return. We will work on Chapter 6 review
on Wednesday. Test on Thursday
Binder check on Test Day
All note and assignments must be current to
earn the 50 points available which is 10% of
your grade. 10% off per day for late
binders.