What is expand (sqrt(2)x^2-pixy^3)^2 ?

The solution to expand (sqrt(2)x^2-pixy^3)^2 is 2x^4-2sqrt(2)pix^3y^3+pi^2x^2y^6

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expand (sqrt(2)x^2-pixy^3)^2

expand

(2 x^{2} - π x y^{3})^{2}

2 x^{4} - 22 π x^{3} y^{3} + π^{2} x^{2} y^{6}

Solution steps

(2 x^{2} - π x y^{3})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 2 x^{2}, b = π x y^{3}

= (2 x^{2})^{2} - 22 x^{2} π x y^{3} + (π x y^{3})^{2}

Simplify

(2 x^{2})^{2} - 22 x^{2} π x y^{3} + (π x y^{3})^{2} : 2 x^{4} - 22 π x^{3} y^{3} + π^{2} x^{2} y^{6}

= 2 x^{4} - 22 π x^{3} y^{3} + π^{2} x^{2} y^{6}

(3 y d x + 6 d x - x d y = 0) \frac{1}{x d y}

W (x - 3, x + 3)

(e^{2 x} - e^{4 x})^{2}

\frac{( 6 x + 1 ) ( x + 1 )}{2 x ( 2 x + 1 )}

sin (3 (t - π))

What is expand (sqrt(2)x^2-pixy^3)^2 ?
The solution to expand (sqrt(2)x^2-pixy^3)^2 is 2x^4-2sqrt(2)pix^3y^3+pi^2x^2y^6