1. Lesson 8-4 Warm-Up

2. “Multiplying Special Cases” (8-4)
What are “squares of a binomial”? How do you square a binomial?
Square of a Binomials: a binomial squared
Example: (a + b)2
Method 1: To square a binomial, multiply the binomial by itself. Then, use an area model or the FOILing method.
Example: Simplify (a + b)2.
Method 2: RULE: To square a binomial, use the following formulas (the square of the first term plus twice the product of the first and second term plus the square of the last term):
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2 S

3. (y + 11)2 = (y + 11)(y + 11) Break into a multiplication problem
Multiplying Special Cases
LESSON 8-4
Additional Examples
a. Find (y + 11)2.
(y + 11)2 = (y + 11)(y + 11) Break into a multiplication problem
= (y)2 + (2)y(11) + (11)2 Substitute a with y and b with 11 in the rule
a2 + 2ab + b2.
= y2 + 22y Simplify.
b. Find (3w – 6)2.
= (3w)2 + 2(3w)(-6) + (-6)2 Substitute a with 3w and b with -6 in the
rule a2 + 2ab + b2.
= 9w2 – 36w + 36 Simplify.

4. Multiplying Special Cases
LESSON 8-4
Additional Examples
Among guinea pigs, the black fur gene (B) is dominant and the white fur gene (W) is recessive. This means that a guinea pig with at least one dominant gene (BB or BW) will have black fur. A guinea pig with two recessive genes (WW) will have white fur.
The square below models the possible combinations of color genes that parents who carry both genes can pass on to their offspring. Since WW is of the outcomes, the probability that a guinea pig has white fur is . 1 4
BB BW
BW WW B W
B W

5. ( B + W)2 = ( B)2 – 2( B)( W) + ( W)2 Square the binomial. Use
Multiplying Special Cases
LESSON 8-4
Additional Examples
(continued)
You can also model the probabilities found in the Punnett square with the expression ( B + W)2. Show that this product gives the same result. 1 2 1 2
( B + W)2 = ( B)2 – 2( B)( W) + ( W) Square the binomial. Use
B for a and W for b
in (a + b)2 = a2 + 2ab + b2 1 2 1 2 1 2
= B BW + W Simplify. 1 4 2
The expressions B2 and W 2 indicate the probability that offspring
will have either two dominant genes or two recessive genes is . The expression BW indicates that there is chance that the offspring will inherit both genes. These are the same probabilities shown in the model. 1 4 2

6. a. Find 812 using mental math.
Multiplying Special Cases
LESSON 8-4
Additional Examples
a. Find 812 using mental math.
812 = (80 + 1)2
= (80)2 + 2(80)(1) + (1)2 Substitute 80 for a and 1 for b in the rule
(a + b)2 = a2 + 2ab + b2.
= = 6561 Simplify.
b. Find 592 using mental math.
592 = (60 – 1)2
= (60)(-1) + (-1)2 Substitute 80 for a and 1 for b in the rule (a + b)2 = a2 + 2ab + b2.
= 3600 – = 3481 Simplify.

7. “Special Cases” (8-4)
What is the “difference of squares”? How do you find the “difference of squares”?
Difference of Squares: the product of the sum and difference of the same two terms
Example: (a + b)(a - b)
Rule: To find the difference of squares, use an area model or the FOILing method. The FOILing method is used below.
(a + b)(a - b) = a(a) + a(-b) + b(a) + b(-b) = a2 – ab + ab - b2
= a2 - b2
Notice that the products of the Outside and Inside of FOIL cancel each other out (in other words, equal zero). So, the product of the sum and difference of the same two terms is the difference of their squares. S

8. Multiplying Special Cases
LESSON 8-4
Additional Examples
Find (p4 – 8)(p4 + 8).
(p4 – 8)(p4 + 8) = (p4)2 – (8)2 Use (a + b)(a - b) = a2 - b2 where a = p4
and b = 8 .
= p8 – 64 Simplify.

9. 43 • 37 = (40 + 3)(40 – 3) Express each factor using 40 and 3. This
Multiplying Special Cases
LESSON 8-4
Additional Examples
Find 43 • 37.
43 • 37 = (40 + 3)(40 – 3) Express each factor using 40 and 3. This
models (a + b)(a - b) = a2 - b2 where a = 40
and b = 3 .
= (40)2 – (3)2 Use (a + b)(a - b) = a2 - b2
= 1600 – 9 = 1591 Simplify.

10. Find each square. 1. (y + 9)2 2. (2h – 7)2 3. 412 4. 292
Multiplying Special Cases
LESSON 8-4
Lesson Quiz
Find each square.
1. (y + 9)2 2. (2h – 7)2
5. Find (p3 – 7)(p3 + 7). 6. Find 32 • 28.
y2 + 18y + 81
4h2 – 28h + 49
1681
841
p6 – 49
896