Question

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

Answer 1

@nincompoop

Answer 2

@bibby

Answer 3

@undeadknight26

Answer 4

@kirbykirby

Answer 5

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

Answer 6

And how will I solve that?

Answer 7

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

So you have \(y+y^3\)

Answer 8

Okay what do I do after that?

Answer 9

factor \(y+y^3\)

Answer 10

Y(y+y^2)

Answer 11

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

Answer 12

I'm not understanding

Answer 13

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

Answer 14

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

Answer 15

Close

\[\large y(1+y^2)\]

\[\large (y)(1+(y)^2)\]

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

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

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

Answer 16

Okay what'd you do for the first step?

Answer 17

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

Answer 18

@jim_thompson5910

Answer 19

how about factoring this