What is (y^2x)(ysin(xy)-(y^3-2x^3)/(x^2y)) ?

The solution to (y^2x)(ysin(xy)-(y^3-2x^3)/(x^2y)) is (y(y^2x^2sin(xy)-y^3+2x^3))/x

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simplify (y^2x)(ysin(xy)-(y^3-2x^3)/(x^2y))

simplify

(y^{2} x) (y sin (x y) - \frac{y ^{3} - 2 x ^{3}}{x ^{2} y})

\frac{y ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{x}

Solution steps

(y^{2} x) (y sin (x y) - \frac{y ^{3} - 2 x ^{3}}{x ^{2} y})

Join

y sin (x y) - \frac{y ^{3} - 2 x ^{3}}{x ^{2} y} : \frac{y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3}}{x ^{2} y}

= y^{2} x \frac{y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3}}{x ^{2} y}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ^{2} x ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{x ^{2} y}

Apply exponent rule:

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

y^{2} = yy

= \frac{yy x ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{x ^{2} y}

Cancel the common factor:

y

= \frac{y x ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{x ^{2}}

Apply exponent rule:

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

x^{2} = xx

= \frac{y x ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{xx}

Cancel the common factor:

x

= \frac{y ( y ^{2} x ^{2} sin ( x y ) - y ^{3} + 2 x ^{3} )}{x}

(x + 5 + 2)^{2}

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

V (- 4, - 3)

(x + 1 - i) (x + 1 + i)

What is (y^2x)(ysin(xy)-(y^3-2x^3)/(x^2y)) ?
The solution to (y^2x)(ysin(xy)-(y^3-2x^3)/(x^2y)) is (y(y^2x^2sin(xy)-y^3+2x^3))/x