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Mathematics 28 Online
OpenStudy (anonymous):

Factor and simplify the algebraic expression (X+9)^(1/4)+(x+9)^(3/4)

OpenStudy (anonymous):

@nincompoop

OpenStudy (anonymous):

@bibby

OpenStudy (anonymous):

@undeadknight26

OpenStudy (anonymous):

@kirbykirby

OpenStudy (kirbykirby):

Maybe it helps if you think of a substitution \((x+9)^{1/4}=y\)

OpenStudy (anonymous):

And how will I solve that?

OpenStudy (kirbykirby):

If \((x+9)^{1/4}=y\), then \((x+9)^{3/4}=\left((x+9)^{1/4}\right)^3=y^3\) So you have \(y+y^3\)

OpenStudy (anonymous):

Okay what do I do after that?

OpenStudy (kirbykirby):

factor \(y+y^3\)

OpenStudy (anonymous):

Y(y+y^2)

OpenStudy (kirbykirby):

almost, \(y(1+y^2)\), then try substitution back what y is in its x-variable

OpenStudy (anonymous):

I'm not understanding

OpenStudy (kirbykirby):

plug back \(y=(x+9)^{1/4}\) into the above result

OpenStudy (anonymous):

Y(x+9)^(1/4)

jimthompson5910 (jim_thompson5910):

Close \[\large y(1+y^2)\] \[\large (y)(1+(y)^2)\] \[\large ((x+9)^{1/4})(1+((x+9)^{1/4})^2)\] \[\large (x+9)^{1/4}*(1+(x+9)^{2/4})\] \[\large (x+9)^{1/4}*(1+(x+9)^{1/2})\]

OpenStudy (anonymous):

Okay what'd you do for the first step?

OpenStudy (anonymous):

Never mind it get it, can you give me another problem so I can do it on my own

OpenStudy (anonymous):

@jim_thompson5910

jimthompson5910 (jim_thompson5910):

how about factoring this |dw:1410988085575:dw|

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