What is (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2) ?

The solution to (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2) is 2u(2v^2-u)

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simplify (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2)

simplify

\frac{3 u ^{4} v ^{4} - 2 u ^{5} v ^{2} + ( u ^{2} v ^{2} ) ^{2}}{u ^{3} v ^{2}}

2 u (2 v^{2} - u)

Solution steps

\frac{3 u ^{4} v ^{4} - 2 u ^{5} v ^{2} + ( u ^{2} v ^{2} ) ^{2}}{u ^{3} v ^{2}}

Simplify

3 u^{4} v^{4} - 2 u^{5} v^{2} + (u^{2} v^{2})^{2} : 4 u^{4} v^{4} - 2 u^{5} v^{2}

= \frac{4 u ^{4} v ^{4} - 2 u ^{5} v ^{2}}{u ^{3} v ^{2}}

Factor

4 u^{4} v^{4} - 2 u^{5} v^{2} : 2 u^{4} v^{2} (2 v^{2} - u)

= \frac{2 u ^{4} v ^{2} ( 2 v ^{2} - u )}{u ^{3} v ^{2}}

Cancel the common factor:

v^{2}

= \frac{2 u ^{4} ( 2 v ^{2} - u )}{u ^{3}}

Apply exponent rule:

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

u^{4} = u^{3} u

= \frac{2 u ^{3} u ( 2 v ^{2} - u )}{u ^{3}}

Cancel the common factor:

u^{3}

= 2 u (2 v^{2} - u)

\frac{x ^{2} - x - 2}{x + 1}

\frac{9 ^{5}}{9 ^{3}}

(5 + 36)^{2}

\frac{96}{100}

(x + 1) (y + 1)

What is (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2) ?
The solution to (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2) is 2u(2v^2-u)