1. Objective
Find special products of binomials.

2. Check It Out! Example 1
Multiply.
A. (x + 6)2
B. (a + 4)2
(x + 6)(x + 6)
(x + 4)(x + 4)
x2 + 4x + 4x + 42
x2 + 6x + 6x + 62
x2 + 8x + 16
x2 + 12x + 36
Do you see a pattern?
(a + b)2 = a2 + 2ab + b2

4. Check It Out! Example 1
Multiply.
A. (x + 7)2
Use the rule for (a + b)2.
(a + b)2 = a2 + 2ab + b2
Identify a and b: a = x and b = 7.
(x + 7)2 = x2 + 2(x)(7) + 72
= x2 + 14x + 49
Simplify.
B. (5a + b)2
Use the rule for (a + b)2.
(a + b)2 = a2 + 2ab + b2
Identify a and b: a = 5a and b = b.
(5a + b)2 = (5a)2 + 2(5a)(b) + b2
= 25a2 + 10ab + b2
Simplify.

6. Example 2: Finding Products in the Form (a – b)2
Multiply.
A. (x – 6)2
Use the rule for (a – b)2.
(a – b)2 = a2 – 2ab + b2
Identify a and b: a = x and b = 6.
(x – 6)2 = x2 – 2x(6) + (6)2
= x2 – 12x + 36
Simplify.
B. (4m – 10)2
Use the rule for (a – b)2.
Identify a and b: a = 4m and b = 10.
(a – b)2 = a2 – 2ab + b2
(4m – 10)2 = (4m)2 – 2(4m)(10) + (10)2
= 16m2 – 80m + 100
Simplify.

8. Example 3: Finding Products in the Form (a + b)(a – b)
Multiply.
A. (x + 4)(x – 4)
Use the rule for (a + b)(a – b).
(a + b)(a – b) = a2 – b2
Identify a and b: a = x and b = 4.
(x + 4)(x – 4) = x2 – 42
= x2 – 16
Simplify.
B. (p2 + 8q)(p2 – 8q)
Use the rule for (a + b)(a – b).
(a + b)(a – b) = a2 – b2
Identify a and b: a = p2 and b = 8q.
(p2 + 8q)(p2 – 8q) = p4 – (8q)2
= p4 – 64q2
Simplify.

9. Example 1C: Finding Products in the Form (a + b)2
Multiply.
C. (5 + m2)2
Use the rule for (a + b)2.
(a + b)2 = a2 + 2ab + b2
Identify a and b: a = 5 and b = m2.
(5 + m2)2 = (5)(m2) + (m2)2
= m2 + m4
Simplify.

10. Example 2: Finding Products in the Form (a – b)2
Multiply.
C. (2x – 5y)2
Use the rule for (a – b)2.
(a – b)2 = a2 – 2ab + b2
Identify a and b: a = 2x and b = 5y.
(2x – 5y)2 = (2x)2 – 2(2x)(5y) + (5y)2
= 2x2 – 20xy +25y2
Simplify.