Factor the expression by removing the common factor with the smaller exponent. 8x3(5x – 4)^(3/2) – 4x(5x – 4)^(-1/2) Factor the expression by removing the common factor with the smaller exponent. (Factor your answer completely.) 8x3(5x – 4)^(3/2) – 4x(5x– 4)^(-1/2)  

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Factor `8x^3(5x-4)^(3/2)-4x(5x-4)^((-1)/2)` :

Factor out `4x(5x-4)^((-1)/2)`

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`4x(5x-4)^((-1)/2)[2x^2(5x-4)^2-1]`

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You could expand, but it is usually not a good idea:

`4x(5x-4)^((-1)/2)[50x^4-80x^3+32x^2-1]`

Or recognize the difference of two squares:

`4x(5x-4)^((-1)/2)[(2x(5x-4)+1)(2x(5x-4)-1)]`

`4x(5x-4)^((-1)/2)[(10x^2-8x+1)(10x^2-8x-1)]`

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Thus fully factored we get:

`4x(5x-4)^((-1)/2)[(10x^2-8x+1)(10x^2-8x-1)]`

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Factor `8x^3(5x-4)^(3/2)-4x(5x-4)^((-1)/2)` :

Factor out `4x(5x-4)^((-1)/2)`

---------------------------------

`4x(5x-4)^((-1)/2)[2x^2(5x-4)^2-1]`

---------------------------------

You could expand, but it is usually not a good idea:

`4x(5x-4)^((-1)/2)[50x^4-80x^3+32x^2-1]`

Or recognize the difference of two squares:

`4x(5x-4)^((-1)/2)[(2x(5x-4)+1)(2x(5x-4)-1)]`

`4x(5x-4)^((-1)/2)[(10x^2-8x+1)(10x^2-8x-1)]`

-----------------------------------------------

Thus fully factored we get:

`4x(5x-4)^((-1)/2)[(10x^2-8x+1)(10x^2-8x-1)]`

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