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...
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)
1 Answer
embizze | High School Teacher | (Level 2) Educator Emeritus
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)]`