Multiplying Special Cases

Chapter 8, Section 4• Simplify each product using FOIL.

1. (x + 2)(x + 5) 2. (2x – 1)(x + 2)

• Simplify each product using FOIL.

3. (r + 6)(r – 4) 4. (4b – 2)(b + 3)

• Simplify each product using FOIL. Write in standard form.

5. (9y2 + 2)(y2 – y – 1)

Chapter 8, Section 4• Simplify each product using FOIL.

1. (x + 2)(x + 5) 2. (2x – 1)(x + 2)

x² + 7x + 10 2x² + 3x - 2

• Simplify each product using FOIL.

3. (r + 6)(r – 4) 4. (4b – 2)(b + 3)

r² + 2r – 24 4b² + 10b - 6

• Simplify each product using FOIL. Write in standard form.

5. (9y2 + 2)(y2 – y – 1)

9y⁴ – 9y³ – 7y² - 2y - 2

8.4 Multiplying Special Cases• The Square of a Binomial

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

The square of a binomial is the square of the first term plus twice the product of the two terms plus the square of the last term.

(a + b)(a – b) = a2 – b2

• The product of the sum and difference of the same two terms is the difference of their squares.

Squaring a Binomiala. Find (x + 7)2.

b. Find (4k – 3)2.

2( 7)x 2 22 (7) 7x x 2 14 49x x

2(4 3)k 2 2(4 ) 2(4 )(3) 3k k 216 24 9k k

The Difference of Squares

• (a + b)(a – b) = a2 – b2

• The product of the sum and difference of the same two terms is the difference of their squares.

Multiplying Using FOIL• Find (t3 – 6)(t3 + 6)

3 3( 6)( 6)t t 3 2 2( ) (6)t 6 36t