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 Find (5q + 9r)2 Square of a Sum Answer: Simplify.

Example 2 A. Find (3c – 4)2 Square of a Difference Answer: Simplify. B. Find (6e – 6f)2 Square of a Difference Answer: Simplify.

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: Homework: 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