What is (27c^4d^7+15c^3d^5)/(3c^2d^3) ?

The solution to (27c^4d^7+15c^3d^5)/(3c^2d^3) is cd^2(9cd^2+5)

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simplify (27c^4d^7+15c^3d^5)/(3c^2d^3)

simplify

\frac{27 c ^{4} d ^{7} + 15 c ^{3} d ^{5}}{3 c ^{2} d ^{3}}

c d^{2} (9 c d^{2} + 5)

Solution steps

\frac{27 c ^{4} d ^{7} + 15 c ^{3} d ^{5}}{3 c ^{2} d ^{3}}

Factor

27 c^{4} d^{7} + 15 c^{3} d^{5} : 3 c^{3} d^{5} (9 c d^{2} + 5)

= \frac{3 c ^{3} d ^{5} ( 9 c d ^{2} + 5 )}{3 c ^{2} d ^{3}}

Cancel the common factor:

3

= \frac{c ^{3} d ^{5} ( 9 c d ^{2} + 5 )}{c ^{2} d ^{3}}

Apply exponent rule:

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

c^{3} = c^{2} c

= \frac{c ^{2} c d ^{5} ( 9 c d ^{2} + 5 )}{c ^{2} d ^{3}}

Cancel the common factor:

c^{2}

= \frac{c d ^{5} ( 9 c d ^{2} + 5 )}{d ^{3}}

Apply exponent rule:

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

d^{5} = d^{3} d^{2}

= \frac{c d ^{3} d ^{2} ( 9 c d ^{2} + 5 )}{d ^{3}}

Cancel the common factor:

d^{3}

= c d^{2} (9 c d^{2} + 5)

3 x^{2} - 17 x + 20

\frac{1}{20} + \frac{1}{12}

9 t (t + 2) - 3 t (t - 2) = 2 (t + 4) (t + 6)

\frac{12 !}{( 12 - 4 ) ! 4 !}

x^{3} - 3 x^{2}

What is (27c^4d^7+15c^3d^5)/(3c^2d^3) ?
The solution to (27c^4d^7+15c^3d^5)/(3c^2d^3) is cd^2(9cd^2+5)