Lesson 8-8

Lesson 8-8

Special Products

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Objectives

• Find the squares of sums and differences

• Find the product of a sum and a difference

Vocabulary

• Difference of squares – two perfect squares separated by a subtraction sign:a2 – b2 = (a + b)(a - b) or (a – b)(a + b).

Multiplying Special Polynomials

Squares of like polynomials in the following forms,where a and b are constants

• Sums: (ax + b)2

– (ax + b)(ax + b) = a2x2 + abx + abx + b2

= a2x2 + 2abx + b2

• Differences: (ax – b)2

– (ax – b)(ax – b) = a2x2 – abx – abx + b2

= a2x2 – 2abx + b2

• One of Each: (ax – b)(ax + b) or (ax + b)(ax – b) – (ax – b)(ax + b) = a2x2 + abx – abx – b2

= a2x2 – b2

Example 1a

Find (7z + 2)2

Square of a Sum

Answer: Simplify.

Check Check your work by using the FOIL method.

F O I L

Example 1b

Square of a Sum

Find (5q + 9r)2

Answer: Simplify.

Example 2

A. Find (3c – 4)2

Square of a Difference

Answer: Simplify.

Square of a Difference

Answer: Simplify.

B. Find (6e – 6f)2

Example 3

Geometry Write an expression that represents the area of a square that has a side length of (2x + 12) units.

The formula for the area of a square is

Area of a square

Simplify.

Answer: The area of the square is square units.

Example 4a

A. Find (9d – 4)(9d + 4)

Product of a Sum and a Difference

Answer: Simplify.

Example 4b

B. Find (10g + 13h3)(10g – 13h3)

Product of a Sum and a Difference

Answer:

Simplify.

Summary & Homework

• Summary:– Square of a Sum (a + b)^2 = a^2 + 2ab + b^2– Square of a Difference (a- b)^2 = a62 – 2ab - b^2– Product of a Sum and a Difference (a-b)(a=b) =

(a+b)(a-b) = a^2 +b^2

• Homework: – pg. 462 14-48 even