What is r(3r^2-s)+s(r-r^4) ?

The solution to r(3r^2-s)+s(r-r^4) is 3r^3-r^4s

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simplify r(3r^2-s)+s(r-r^4)

simplify

r (3 r^{2} - s) + s (r - r^{4})

3 r^{3} - r^{4} s

Solution steps

r (3 r^{2} - s) + s (r - r^{4})

Expand

r (3 r^{2} - s) : 3 r^{3} - rs

= 3 r^{3} - rs + s (r - r^{4})

Expand

s (r - r^{4}) : rs - r^{4} s

= 3 r^{3} - rs + rs - r^{4} s

Add similar elements:

- rs + rs = 0

= 3 r^{3} - r^{4} s

(27 x^{- 3})^{\frac{1}{3}}

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\frac{x ^{3}}{3} + \frac{3}{x ^{3}}