Page 111 - Math Course 2 (Book 1)

Polynomial Expressions

Mo. 3

Lesson 11 Square of a Difference

Words The square of a – b is the square of
KEY CONCEPTS: a minus twice the product of a and b
1. Find squares of sums and differences. plus the square of b
2. Find the product of a sum and a difference.
Symbols (a – b) = (a – b)(a – b) = a – 2ab + b 2
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2
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Examples (x – 4) = x –2x(4) + 4 = x – 8x + 16
MO. 3 - L11a
Finding the Squares of Sums Product of a Sum and
and Differences Difference

Words The product of a + b and a – b is the
Vocabulary A-Z square of a minus the square of b.
Let us learn some vocabulary
Symbols (a + b)(a – b) = (a – b)(a + b) = a – b 2
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2
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Examples (x + 9)(x – 9) = x – 9 = x – 81
Difference of two squares
the pattern for the product of the sum and difference
of the same two terms, (a + b)(a – b). Let’s Begin

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(a + b)(a – b) The resulting product, a – b ,
is called the different of two squares.
Square of a Sum
a + (–b)
a –b
Example
a a 2 –ab = 2 –ab + 2
a + b a + ab + –b
Find (7z + 2) 2
b ab –b 2
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= a 2 + –b 2 (a + b) = a + 2ab + b 2
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(7z + 2) = (7z) + 2(7z)(2) + (2) a = 7z and
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= a + (–b ) b = 2.
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= a – b 2 Answer 49z + 28z + 4 Simplify.
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Key Concept Square of a Difference
Square of a Sum Example

Words The square of a + b is the square of a Find (3c – 4) .
2
plus twice the product of a and b plus
the square of b (a – b) = a – 2ab + b 2
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2
Symbols (a + b) = (a + b)(a + b) = a + 2ab + b 2 (3c – 4) = (3c) – 2(3c)(4) + (4) a = 3c and b = 4
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Examples (x + 7) = x + 2x(7) + 7 = x + 14x + 49 Answer 9c – 24c + 16 Simplify.
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