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## Lesson 8-8

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**Lesson 8-8**Special Products**Transparency 8**Click the mouse button or press the Space Bar to display the answers.**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**Square of a Sum**F O I L Simplify. Answer: Example 1a Find (7z + 2)2 Check Check your work by using the FOIL method.**Square of a Sum**Simplify. Answer: Example 1b Find (5q + 9r)2**Square of a Difference**Square of a Difference Simplify. Simplify. Answer: Answer: Example 2 A. Find (3c – 4)2 B. Find (6e – 6f)2**The formula for the area of a square is**Area of a square Simplify. Answer: The area of the square is square units. Example 3 Geometry Write an expression that represents the area of a square that has a side length of (2x + 12) units.**Product of a Sum and a Difference**Answer: Simplify. 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)**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