1. Lesson 8-8
Special Products

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Transparency 8

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 + b = a2x2 + 2abx + b2
Differences: (ax – b)2
(ax – b)(ax – b) = a2x2 – abx – abx + b = a2x2 – 2abx + b2
One of Each: (ax – b)(ax + b) or (ax + b)(ax – b)
(ax – b)(ax + b) = a2x2 + abx – abx – b = a2x2 – b2

7. 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

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

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

10. 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.

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

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

13. 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:
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