1. BELL-WORK (x – 5)(x + 5) = x2 – 25 (b) (3x – 2)(3x + 2) = 9x2 – 4
(4x + y)(4x – y) = 16x2 – y2
We usually expect a trinomial when we multiply binomials, but this is a special case!
Do you notice a pattern when (a + b) is multiplied by
(a – b)?
This relationship is known as the difference of two squares.
Difference of two squares (DOTS):
(a + b)(a – b) = a2 – b2

2. Difference of Two Squares
Use DOTS to find the product:
(x + 9)(x – 9) = x2 – 81
(6 + m2)(6 – m2) = -m2 + 36
(3c – 4)(3c + 4) = 9c2 – 16
(9v3 + w4)(9v3 – w4) = 81v6 – w8

3. Factoring a Binomial Use DOTS to factor binomials. (a) d2 – 49 d2 – 72
(b) k2 – 25
k2 – 52
(k + 5)(k – 5)
(c) c4 – 144
(c2)2 – 122
(c2 + 12)(c2 – 12)
(d) 4a2 – 64
4[(a)2 – 42]
4 (a + 4)(a – 4)

4. Factoring a Binomial 4p2 – 49 (2p)2 – 72 (2p + 7)(2p – 7) 81r2 – 1
(9r + 1)(9r – 1)
36v2 – 25
(6v)2 – 52
(6v + 5)(6v – 5)
(d) 64q2 – 81
(8q)2 – 92
(8q + 9)(8q – 9)
16x2 – 121
(4x)2 – 112
(4x + 11)(4x – 11)
(f) 2h2 – 2 = 2(h2 – 1)
2[(h)2 – 12]
2(h + 1)(h – 1)

5. DOTS & Mental Math 38×42 (40 – 2)(40 + 2) 402 – 22 1600 – 4 1596 64×56
(60 + 4)(60 – 4)
602 – 42
3600 – 16
3584

6. DOTS & Mental Math 399×401 (400 + 1)(400 – 1) 4002 – 12 160000 – 1
159999
303×297
( )(300 – 3)
3002 – 32
90000 – 9
89991