Factoring negative roots

[xcoolcatx06]

Ok, on my first pre-calculus test, I was given the question: (x)^-1/2(x+1)^1/2 + (x)^1/2(x+1)^-1/2. How do I factor this? Thanks a lot.


Edit: another question I can't figure out is: Factor: 16x^3n - 250y^6

Am I missing an important law of exponents? thanks

 

[mmm4444bot]

Please enclose exponents within parentheses, when they are ratios, products, negative, etc.

x^(-1/2) * (x + 1)^(1/2) + x^(1/2) * (x + 1)^(-1/2)

One approach to factoring this expression is to examine the radical form.

\(\displaystyle \frac{\sqrt{x \;+\; 1}}{\sqrt{x}} \;+\; \frac{\sqrt{x}}{\sqrt{x \;+\; 1}}\)

Combine these ratios.

\(\displaystyle \frac{2x \;+\; 1}{\sqrt{x} \cdot \sqrt{x \;+\; 1}}\)

Can you factor this ratio into a product of three factors? Then switch back to exponential form.

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16x^(3n) - 250y^6

With this one, a little manipulation gives us a factor that is a difference of cubes. Start by factoring out a 2, and rewrite what's left as cubes.

2 * (2^3 * [x^n]^3 - 5^3 * [y^2]^3)

Cheers,

~ Mark