Factoring the Sum

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Factoring the Sum Difference of Two Cubes
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This is a piece of cake, if you have perfect
cubes. What are perfect cubes? Something
times something times something. Where the
something is a factor 3 times. 8 is 2 ? 2 ? 2,
so 8 is a perfect cube. x6 is x2 ? x2 ? x2 so
x6 is a perfect cube. It is easy to see if a
variable is a perfect cube, how? See if the
exponent is divisible by 3. Its harder
for integers.
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The sum or difference of two cubes will factor
into a binomial ? trinomial.
same sign
always
always opposite
same sign
always
always opposite
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Now we know how to get the signs, lets work
on what goes inside.
Square this term to get this term.
Cube root of 1st term
Cube root of 2nd term
Product of cube root of 1st term and cube root of
2nd term.
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Try one.
Make a binomial and a trinomial with the correct
signs.
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Try one.
Cube root of 1st term
Cube root of 2nd term
7
Try one.
Square this term to get this term.
8
Try one.
Multiply 3x an 5 to get this term.
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Try one.
Square this term to get this term.
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Try one.
You did it!
Dont forget the first rule of factoring is to
look for the greatest common factor.
I hope you took notes!
11

• Factor each of the following polynomials
  completely.
• 8x3 27
• (2x 3)((2x)2 (2x)(3) (3)2) ? Use the
  pattern
• a3 b3 (a b)(a2 ab b2)
• (2x 3)(4x2 6x 9)
• b) 9x4 9x
• 9x(x3 1) ? First remove the GCF
• 9x(x 1)(x2 x 1) ? Factor the difference
  of cubes x3 1