What is expand (y-x)^2*((2x^3)/3+(4x^2y)/3) ?

The solution to expand (y-x)^2*((2x^3)/3+(4x^2y)/3) is (2x^5-6y^2x^3+4y^3x^2)/3

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expand (y-x)^2*((2x^3)/3+(4x^2y)/3)

expand

(y - x)^{2} \cdot (\frac{2 x ^{3}}{3} + \frac{4 x ^{2} y}{3})

\frac{2 x ^{5} - 6 y ^{2} x ^{3} + 4 y ^{3} x ^{2}}{3}

Solution steps

(y - x)^{2} (\frac{2 x ^{3}}{3} + \frac{4 x ^{2} y}{3})

Expand

(y - x)^{2} : y^{2} - 2 y x + x^{2}

= (y^{2} - 2 y x + x^{2}) (\frac{2 x ^{3}}{3} + \frac{4 x ^{2} y}{3})

Distribute parentheses

= y^{2} \frac{2 x ^{3}}{3} + y^{2} \frac{4 x ^{2} y}{3} - 2 y x \frac{2 x ^{3}}{3} - 2 y x \frac{4 x ^{2} y}{3} + x^{2} \frac{2 x ^{3}}{3} + x^{2} \frac{4 x ^{2} y}{3}

Simplify

y^{2} \frac{2 x ^{3}}{3} + y^{2} \frac{4 x ^{2} y}{3} - 2 y x \frac{2 x ^{3}}{3} - 2 y x \frac{4 x ^{2} y}{3} + x^{2} \frac{2 x ^{3}}{3} + x^{2} \frac{4 x ^{2} y}{3} : \frac{2 x ^{5} - 6 y ^{2} x ^{3} + 4 y ^{3} x ^{2}}{3}

= \frac{2 x ^{5} - 6 y ^{2} x ^{3} + 4 y ^{3} x ^{2}}{3}

\frac{0.84826 ( s - 2.1598 ) ( s + 0.1 )}{s}

x (x^{5} e^{13 x} + 4)

(cos (t) + i sin (t))^{2}

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

\frac{d ^{2}}{d x ^{2}} (x^{4}) + (x - 1)^{4}

What is expand (y-x)^2*((2x^3)/3+(4x^2y)/3) ?
The solution to expand (y-x)^2*((2x^3)/3+(4x^2y)/3) is (2x^5-6y^2x^3+4y^3x^2)/3