What is ((4r^6-100r^3))/((24r^3+288r^2+840r)) ?

The solution to ((4r^6-100r^3))/((24r^3+288r^2+840r)) is (r^2(r^3-25))/(6(r+5)(r+7))

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simplify ((4r^6-100r^3))/((24r^3+288r^2+840r))

simplify

\frac{( 4 r ^{6} - 100 r ^{3} )}{( 24 r ^{3} + 288 r ^{2} + 840 r )}

\frac{r ^{2} ( r ^{3} - 25 )}{6 ( r + 5 ) ( r + 7 )}

Solution steps

\frac{4 r ^{6} - 100 r ^{3}}{24 r ^{3} + 288 r ^{2} + 840 r}

Factor

4 r^{6} - 100 r^{3} : 4 r^{3} (r^{3} - 25)

= \frac{4 r ^{3} ( r ^{3} - 25 )}{24 r ^{3} + 288 r ^{2} + 840 r}

Factor

24 r^{3} + 288 r^{2} + 840 r : 24 r (r + 5) (r + 7)

= \frac{4 r ^{3} ( r ^{3} - 25 )}{24 r ( r + 5 ) ( r + 7 )}

Factor the number:

24 = 4 \cdot 6

= \frac{4 r ^{3} ( r ^{3} - 25 )}{4 \cdot 6 r ( r + 5 ) ( r + 7 )}

Cancel the common factor:

4

= \frac{r ^{3} ( r ^{3} - 25 )}{6 r ( r + 5 ) ( r + 7 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

r^{3} = r r^{2}

= \frac{r r ^{2} ( r ^{3} - 25 )}{6 r ( r + 5 ) ( r + 7 )}

Cancel the common factor:

r

= \frac{r ^{2} ( r ^{3} - 25 )}{6 ( r + 5 ) ( r + 7 )}

(\frac{k}{l})^{\frac{1}{2}}

\frac{( x + 5 )}{5} - \frac{( x - 8 x ^{2} )}{x}

\frac{121}{( x - a )} + \frac{1}{( x ^{2} - a ^{2} )}

a^{5} + x^{5}

27 x^{3} - y^{3} + 9 x^{2} y - 3 x y^{2}

What is ((4r^6-100r^3))/((24r^3+288r^2+840r)) ?
The solution to ((4r^6-100r^3))/((24r^3+288r^2+840r)) is (r^2(r^3-25))/(6(r+5)(r+7))