This document provides information about finding the area of squares, using the square of a binomial pattern, using the sum and difference pattern, and examples of applying these patterns to find products of binomial expressions. It introduces shorthand methods for finding products like (a + b)2, (a - b)2, and (a + b)(a - b) more quickly than using the traditional FOIL (First, Outer, Inner, Last) method. Examples are provided to demonstrate finding products like (3x + 4)2, (5x - 2y)2, (t + 5)(t - 5), and using mental math to find 26 • 34. Warm-up problems at the end ask the reader to

2. Area of a Square
 Square with side length a+b
a b
a a 2
ab
b ab b 2
a + 2ab + b
2 2

3. Square of a Binomial Pattern
 Same result as using the previous methods
(Table, Vertical, Horizontal, FOIL) but quicker with
less work (Shortcut!)
(a + b) = a + 2ab + b
2 2 2
(x + 5)2 = x 2 +10x + 25
(a - b) = a - 2ab + b
2 2 2
(x - 3)2 = x - 6x + 9
2

4. Example 1 Use the square of a binomial pattern
Find the product.
a. ( 3x + 4 )2 = ( 3x )2 + 2( 3x ) ( 4 ) + 42 Square of a binomial
pattern
= 9x2 + 24x + 16 Simplify.
b. ( 5x – 2y )2 = ( 5x )2 – 2( 5x ) ( 2y ) + ( 2y )2 Square of a
binomial pattern
= 25x2 – 20xy + 4y2 Simplify.

5. Sum and Difference Pattern
 Find the Product
(x + 2)(x - 2) =
First Outer Inner Last
x × x +x(-2) +2x +2(-2)
x +(-2x) +2x +(-4)
2
x -4
2

6. Sum and Difference Pattern
 Same result as using the previous methods
(Table, Vertical, Horizontal, FOIL) but quicker with
less work (Shortcut!)
(a + b)(a - b) = a - b 2 2
(x + 3)(x - 3) = x - 9 2

7. Example 2 Use the sum and difference pattern
Find the product.
a. ( t + 5 )( t – 5 ) = t2 – 52 Sum and difference
pattern
= t2 – 25 Simplify.
b. ( 3x + y ) ( 3x – y ) = ( 3x )2 – y2 Sum and difference
pattern
= 9x2 – y2 Simplify.

8. Special Products Summary
 Square of a Binomial
(a + b)2 = a2 + 2ab + b2
(a - b) = a - 2ab + b
2 2 2
 Sum and Difference of a Binomial
(a + b)(a - b) = a 2 - b2

9. Example 3 Use special products and mental math
Use special products to find the product 26 • 34 .
SOLUTION
Notice that 26 is 4 less than 30 while 34 is 4 more than 30.
26 • 34 = ( 30 – 4 ) ( 30 + 4 ) Write as product of
difference and sum.
= 302 – 42 Sum and difference
pattern
= 900 – 16 Evaluate powers.
= 884 Simplify.

10. 9.3 Warm-Up (Day 1)
 Find the product
1. (a + 6) 2
2. (n -11) 2
3. (2x +1)(2x -1)

11. 9.3 Warm-Up (Day 2)
 Find the product
1. (4c - 9) 2
1 1
2. (4g + )(4g - )
2 2
3. (1.5y - 3)(1.5y + 3)