What is expand (sqrt(x)+2xy)^3 ?

The solution to expand (sqrt(x)+2xy)^3 is xsqrt(x)+6x^2y+12x^2y^2sqrt(x)+8x^3y^3

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expand (sqrt(x)+2xy)^3

expand

(x + 2 x y)^{3}

x x + 6 x^{2} y + 12 x^{2} y^{2} x + 8 x^{3} y^{3}

Solution steps

(x + 2 x y)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(x + 2 x y)^{3} = (x)^{3} + 3 (x)^{2} \cdot 2 x y + 3 x (2 x y)^{2} + (2 x y)^{3}

= (x)^{3} + 3 (x)^{2} \cdot 2 x y + 3 x (2 x y)^{2} + (2 x y)^{3}

Simplify

(x)^{3} + 3 (x)^{2} \cdot 2 x y + 3 x (2 x y)^{2} + (2 x y)^{3} : x x + 6 x^{2} y + 12 x^{2} y^{2} x + 8 x^{3} y^{3}

= x x + 6 x^{2} y + 12 x^{2} y^{2} x + 8 x^{3} y^{3}

(7 d - 9 e + 2 f) \times 3 f

x (7 x^{2} + 14 x - 11)

(e^{2 t} - e^{t}) (e^{2 t} + e^{t})

\frac{1}{s ( s ^{2} + a ^{2} )}

(2 + 3)^{2}

What is expand (sqrt(x)+2xy)^3 ?
The solution to expand (sqrt(x)+2xy)^3 is xsqrt(x)+6x^2y+12x^2y^2sqrt(x)+8x^3y^3