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Lesson 8-8

Lesson 8-8. Special Products. Transparency 8. Click the mouse button or press the Space Bar to display the answers. Transparency 8a. Objectives. Find the squares of sums and differences Find the product of a sum and a difference. Vocabulary.

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Lesson 8-8

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  1. Lesson 8-8 Special Products

  2. Transparency 8 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 8a

  4. Objectives • Find the squares of sums and differences • Find the product of a sum and a difference

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

  6. 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

  7. 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.

  8. Square of a Sum Simplify. Answer: Example 1b Find (5q + 9r)2

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

  10. 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.

  11. Product of a Sum and a Difference Answer: Simplify. Example 4a A. Find (9d – 4)(9d + 4)

  12. Product of a Sum and a Difference Answer: Simplify. Example 4b B. Find (10g + 13h3)(10g – 13h3)

  13. 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

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