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dmitriy555
[2]
3 years ago
7
Need help factoring this binomial: x^4-1?
Mathematics
Answer
Comment
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2
answers:
marusya05
[52]
3 years ago
8
0
So we notice that is the special factorization known as 'the difference of two perfect squares'
exg
a^2-b^2=(a-b)(a+b) so
x^4=(x^2)^2 and 1=1^2 so
(x^2)^2-(1)^2=(x^2-1)(x^2+1)
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natima
[27]
3 years ago
5
0
Use the difference of squares factorization - that for any numbers a and b, (a-b)(a+b)=a^2-b^2.
We have:
(x^2+1)(x^2-1)=x^4-1
In addition:
(x-1)(x+1)=x^2-1, so we have:
(x^2+1)(x+1)(x-1)
As our complete factorization.
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