Originally Posted by

**Jonboy** Hi everyone! I would like you all to check these problems and if there's an easier way please do give the suggestion. The directions are to simplify.

#1 $\displaystyle 8 + \frac{25}{\sqrt{5}}$

I though I should get one fraction: $\displaystyle \frac{8\sqrt{5}\,+ 25}{\sqrt{5}}$

Rationalize: $\displaystyle \frac{40\,+\,25\sqrt{5}}{5} = \boxed{8 + 5\sqrt{5}}$

# 2 $\displaystyle 9x^3 - 35x^2 - 4x$

$\displaystyle \boxed{x(9x^2 - 35x - 4)}$

I don't see how that can simplify any more... do you agree?

# 3 $\displaystyle 27x^6 + 125y^6 = (3x^2)^3 + (5y^2)^3$

I factored this as: $\displaystyle \boxed{(3x^2 + 5y^2)(9x^4 - 3x^2 5y^2 + 25y^4)}$

# 4 $\displaystyle 4x^3 - 4x^2 - 9x + 9$

Factor by grouping: $\displaystyle 4x^2(x - 1) -9(x - 1) \Rightarrow (4x^2 - 9)(x - 1)$

Which goes to: $\displaystyle \boxed{(2x - 3)(2x + 3)(x - 1)}$

Look good guys/gals?