1. Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1)
3) (2xy + 4x)(-2y + y2)

2. 8.4 Multiplying Binomials – Special Products
Objectives:
To multiply the sum and difference of two expressions
To square a binomial

3. Example 1 Multiply. (x + 6)(x – 6)
= (x)(x) + (x)(-6) + (6)(x) + (6)(-6)
= x2 – 6x + 6x - 36
= x2 - 36

4. Example 2 Multiply. (2x + 4)(2x – 4)
= (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4)
= 4x2 – 8x + 8x - 16
= 4x2 - 16

5. Example 3 Multiply. (-3x + 4y)(-3x – 4y)
= (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y)
= 9x2 + 12xy – 12xy – 16y2
= 9x2 – 16y2

6. Example 4 Multiply. (x + 2)2 = (x + 2)(x + 2)
= (x)(x) + (x)(2) + (2)(x) + (2)(2)
= x2 + 2x + 2x + 4
= x2 + 4x + 4

7. Example 5 Multiply. (x - 3)2 = (x - 3)(x - 3)
= (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3)
= x2 - 3x - 3x + 9
= x2 - 6x + 9

8. Example 6 Multiply. (2x – 3y)2 = (2x – 3y)(2x – 3y)
= (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y)
= 4x2 - 6xy - 6xy + 9y2
= 4x2 - 12xy + 9y2

9. Example 7 812 = (80 + 1)2 = 802 + 2(80 • 1) + 12 Square the binomial.
Multiplying Special Cases
Example 7 4
a. Find 812 using mental math.
812 = (80 + 1)2
= (80 • 1) + 12 Square the binomial.
= = 6561 Simplify.
b. Find 592 using mental math.
592 = (60 – 1)2
= 602 – 2(60 • 1) + 12 Square the binomial.
= 3600 – = 3481 Simplify.
Quick Check

10. Multiplying Special Cases
Example 8
Ex. Find 43 • 37.
43 • 37 = (40 + 3)(40 – 3) Express each factor using 40 and 3.
= 402 – 32 Find the difference of squares.
= 1600 – 9 = Simplify.