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# Help greatly needed

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Find the least common multiple of \(1-x^2\)and \((x-1)^3\). This problem had been bugging me for a bit and I can't figure it out, if someone can help that would be great :)

Feb 9, 2021

### 3+0 Answers

#1
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1  - x^2     = ( x - 1)  ( x + 1)   =    -( 1 - x) (x + 1)  =  -( x + 1) ( x  -1)

Take the  highest power on each  unique  factor between both  polynomials

highest power of  ( x -1)  =  3  =  ( x  -1)^3

highest power of  - (x + 1)  = 1  =   [- (x + 1) ]^1  =  -(x + 1)

LCM  =   -(x + 1) ( x - 1)^3   Feb 9, 2021
edited by CPhill  Feb 9, 2021
#2
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We can rearrange the the first expression as

\$-x^2+1\$

we can factor a \$-1\$

\$-1(x^2-1)\$

\$-(x+1)(x-1)\$

the second expression is

\$(x-1)(x-1)(x-1)\$

that means

\$(x-1)^2*-(x+1)\$

i am really unsure about the finding the least common multiple, because I am really rusty with that part, but the factoring part is definitely correct

Feb 9, 2021
#3
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Thank you CPhil and Guest! I get it now :)

Feb 9, 2021