Over Lesson 8–3

Splash Screen Special Products Lesson 8-4

Then/Now Understand how to find squares and products of sums and differences.

Concept

Example 1 Square of a Sum Find (7z + 2) 2. (a + b) 2 = a 2 + 2ab + b 2 Square of a sum (7z + 2) 2 = (7z) 2 + 2(7z)(2) + (2) 2 a = 7z and b = 2 = 49z z + 4Simplify. Answer: 49z z + 4

Example 1 Find (3x + 2) 2.

Concept

Example 2 Square of a Difference Find (3c – 4) 2. (a – b) 2 = a 2 – 2ab + b 2 Square of a difference (3c – 4) 2 = (3c) 2 – 2(3c)(4) + (4) 2 a = 3c and b = 4 = 9c 2 – 24c + 16Simplify. Answer: 9c 2 – 24c + 16

Example 2 Find (2m – 3) 2.

Example 3 Square of a Difference GEOMETRY Write an expression that represents the area of a square that has a side length of 3x + 12 units. The formula for the area of a square is A = s 2. Answer: The area of the square is 9x x square units. A = s 2 Area of a square A = (3x + 12) 2 s = (3x + 12) A = (3x) 2 + 2(3x)(12) + (12) 2 a = 3x and b = 12 A = 9x x + 144Simplify.

Example 3 GEOMETRY Write an expression that represents the area of a square that has a side length of (3x – 4) units.

Concept

Example 4 Product of a Sum and a Difference Find (9d + 4)(9d – 4). (a + b)(a – b)= a 2 – b 2 (9d + 4)(9d – 4)= (9d) 2 – (4) 2 a = 9d and b = 4 = 81d 2 – 16Simplify. Answer: 81d 2 – 16

Example 4 Find (3y + 2)(3y – 2).

End of the Lesson Homework p. 489 #23-53 odd, 48