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Difference of Two Perfect Squares
6.3 – Factoring “Special”
Polynomials
Objective: TSW factor perfect square
and perfect cube polynomials.
Difference – subtract
Two perfect squares – problem has two perfect
squares in it.
To factor:
1. Square root the first number (goes in first spot
in parenthesis)
2. Square root the second number (goes in second
spot in parenthesis)
3. Opposite signs in each (one + and one - )
Examples: Factor
1. x2 – 81
2. 9x2 – 25
Example 5:
3. 3x2 – 48
4. 2x2 – 2
Perfect Square Trinomials
• First and last terms are perfect squares.
• Middle term is 2(square root of first
term)(square root of last term)
• If this is the case, then it is a perfect square
trinomial
• You can factor these as (ax +b)2 or (ax – b)2
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10/8/2015
Example 6
Example 7
Sum/Difference of Two Perfect Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
8. x3 + 8
9. 27x3 – 1 =
1. Find a and b from your two terms (cube root
them)
2. Plug the values into the formula (a and b will
be positive). The formula takes care of what
needs to be negative.
3. Simplify if you can.
Example 10:
r 3 − 8s 3
Homework
6.3 page 364 #’s 9-63 multiples of 3
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