November 25, 2014
DO NOW: Multiply the binomial by the binomial.
b) (y + 8)(y - 8)
a) (x + 6)(x - 5)
Example (b):
The two binomials are the sum and difference of the same terms.
Their product is a binomial that is a difference of perfect squares.
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November 25, 2014
I. Factoring the Difference of Two Squares (DOTS):
a2 - b2 = (a + b)(a - b)
Perfect Square Whole #'s: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Perfect Square Variables: x2, x4, x6, x8, x10, x12, etc.
WARNING
***Will NOT work for a2 + b2***
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November 25, 2014
Examples: Factor.
a) x2 - 25
b)
x2 - 4
c)
4a2 - b2
d)
16a4 - 25b6
e)
100 - b2
f)
x6 + 25
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November 25, 2014
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November 25, 2014
Remember when you square something - you multiply it by itself!!!!!!!!!
II. Finding the Square of a Sum or Difference:
a) Find:
(x + 3)2
b) Find:
(x - 4)2
Notice: The coefficient of the middle term is double the constant
and the last term is the constant squared.
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November 25, 2014
c) Find:
(x + 6)2
d) Find:
(x - 5)2
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
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November 25, 2014
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November 25, 2014
Lesson Summary:
• Factoring is the reverse process of multiplication. When factoring, it is helpful to look for a GCF that can be pulled out of the polynomial expression.
• Factor the difference of perfect squares a2 ­ b2 as (a ­ b)(a + b).
• When squaring a binomial use the following rules:
(a + b)2 = a2 + 2ab + b2
(a ­ b)2 = a2 ­ 2ab + b2
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