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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. - PowerPoint PPT Presentation
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Lesson 8-8
Special Products
Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.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
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