You have a difference of squares.
In general if you have a² - b², that is equivalent to (a+b)(a-b). Multiply it out if you aren't sure. You'll see that you get a² -ab + ab + b² and the +ab and -ab cancel out.
In your example you have:
1 - 16x^4
This is equivalent to:
1² - (4x²)²
Using the rule above:
(1 - 4x²)(1 + 4x²)
Next notice that you have another difference of squares:
(1² - (2x)²)(1 + 4x²)
Again using the rule, you can split the difference of squares:
(1 - 2x)(1 + 2x)(1 + 4x²)
Unfortunately you can't do much else with the 1+4x², so your expression is fully factored.
2007-10-04 13:34:08
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answer #1
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answered by Puzzling 7
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a^2 - b^2 = (a-b)(a+b)
1-16x^4 = (1 - 4x^2)(1 + 4x^2)
=(1-2x)(1+2x)(1+4x^2)
2007-10-04 13:33:45
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answer #2
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answered by norman 7
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a² - b² = (a+b)(a-b)
1 - 16x^4
= 1² - (4x²)²
= (1+4x²)(1-4x²)
= (1+4x²)(1-(2x)²)
= (1+4x²)(1+2x)(1-2x)
2007-10-04 13:32:28
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answer #3
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answered by gudspeling 7
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(1+4x^2)[(1-2x)(1+2x)]
difference of two squares
hope this helps
2007-10-04 13:33:09
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answer #4
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answered by soul_burner_29 2
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(1-16x^4)
=1-(4x^2)^2
=(1-4x^2)(1+4x^2)
=(1-2x)(1+2x)(1+4x2)
2007-10-04 13:33:14
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answer #5
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answered by jsarkar14 2
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