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

The solution to expand (y-x)^2*((4x^2y)/3) is (4x^2y^3-8x^3y^2+4x^4y)/3

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

expand

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

\frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

Solution steps

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

Apply rule:

(a) = a

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

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

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

Expand

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

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

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

Simplify

\frac{4 x ^{2} y}{3} y^{2} + \frac{4 x ^{2} y}{3} (- 2 y x) + \frac{4 x ^{2} y}{3} x^{2} : \frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

= \frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

2 \cdot (3 - 1)

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

\frac{s ^{2} + 2}{s ( s ^{2} + 4 )}

A (3, 4) B (7, - 1)

2 (- e^{- x} x - e^{- x})

What is expand (y-x)^2*((4x^2y)/3) ?
The solution to expand (y-x)^2*((4x^2y)/3) is (4x^2y^3-8x^3y^2+4x^4y)/3