What is expand ((x^2*y)+((2*x)*y)+(c*x)+(2*c))^3 ?

The solution to expand ((x^2*y)+((2*x)*y)+(c*x)+(2*c))^3 is

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expand ((x^2y)+((2x)y)+(cx)+(2*c))^3

expand

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

x^{6} y^{3} + c^{3} x^{3} + 6 x^{5} y^{3} + 3 c x^{5} y^{2} + 3 c^{2} x^{4} y + 2 c^{3} x^{2} + 12 x^{4} y^{3} + 8 c^{3} + 12 x c^{3} + 8 x^{3} y^{3} + 4 x^{2} c^{3} + 18 c x^{4} y^{2} + 14 c^{2} x^{3} y + 36 c x^{3} y^{2} + 28 c^{2} x^{2} y + 24 x c^{2} y + 24 c x^{2} y^{2} + 4 x^{3} c^{2} y + 8 x^{2} c^{2} y

Solution steps

((x^{2} y) + ((2 x) y) + (c x) + (2 c))^{3}

Simplify

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

= (x^{2} y + 2 x y + c x + 2 c)^{3}

Simplify

(x^{2} y + 2 x y + c x + 2 c)^{3} : (x^{2} y + 2 x y + c x + 2 c) (x^{2} y + 2 x y + c x + 2 c) (x^{2} y + 2 x y + c x + 2 c)

= (x^{2} y + 2 x y + c x + 2 c) (x^{2} y + 2 x y + c x + 2 c) (x^{2} y + 2 x y + c x + 2 c)

Expand

(x^{2} y + 2 x y + c x + 2 c) (x^{2} y + 2 x y + c x + 2 c) : x^{4} y^{2} + c^{2} x^{2} + 4 x^{3} y^{2} + 4 c^{2} + 2 c x^{3} y + 4 x^{2} y^{2} + 4 x c^{2} + 8 c x^{2} y + 8 c x y

= (x^{4} y^{2} + c^{2} x^{2} + 4 x^{3} y^{2} + 4 c^{2} + 2 c x^{3} y + 4 x^{2} y^{2} + 4 x c^{2} + 8 c x^{2} y + 8 c x y) (x^{2} y + 2 x y + c x + 2 c)

Distribute parentheses

= x^{4} y^{2} x^{2} y + x^{4} y^{2} \cdot 2 x y + x^{4} y^{2} c x + x^{4} y^{2} \cdot 2 c + c^{2} x^{2} x^{2} y + c^{2} x^{2} \cdot 2 x y + c^{2} x^{2} c x + c^{2} x^{2} \cdot 2 c + 4 x^{3} y^{2} x^{2} y + 4 x^{3} y^{2} \cdot 2 x y + 4 x^{3} y^{2} c x + 4 x^{3} y^{2} \cdot 2 c + 4 c^{2} x^{2} y + 4 c^{2} \cdot 2 x y + 4 c^{2} c x + 4 c^{2} \cdot 2 c + 2 c x^{3} y x^{2} y + 2 c x^{3} y \cdot 2 x y + 2 c x^{3} yc x + 2 c x^{3} y \cdot 2 c + 4 x^{2} y^{2} x^{2} y + 4 x^{2} y^{2} \cdot 2 x y + 4 x^{2} y^{2} c x + 4 x^{2} y^{2} \cdot 2 c + 4 x c^{2} x^{2} y + 4 x c^{2} \cdot 2 x y + 4 x c^{2} c x + 4 x c^{2} \cdot 2 c + 8 c x^{2} y x^{2} y + 8 c x^{2} y \cdot 2 x y + 8 c x^{2} yc x + 8 c x^{2} y \cdot 2 c + 8 c x y x^{2} y + 8 c x y \cdot 2 x y + 8 c x yc x + 8 c x y \cdot 2 c

Simplify

x^{4} y^{2} x^{2} y + x^{4} y^{2} \cdot 2 x y + x^{4} y^{2} c x + x^{4} y^{2} \cdot 2 c + c^{2} x^{2} x^{2} y + c^{2} x^{2} \cdot 2 x y + c^{2} x^{2} c x + c^{2} x^{2} \cdot 2 c + 4 x^{3} y^{2} x^{2} y + 4 x^{3} y^{2} \cdot 2 x y + 4 x^{3} y^{2} c x + 4 x^{3} y^{2} \cdot 2 c + 4 c^{2} x^{2} y + 4 c^{2} \cdot 2 x y + 4 c^{2} c x + 4 c^{2} \cdot 2 c + 2 c x^{3} y x^{2} y + 2 c x^{3} y \cdot 2 x y + 2 c x^{3} yc x + 2 c x^{3} y \cdot 2 c + 4 x^{2} y^{2} x^{2} y + 4 x^{2} y^{2} \cdot 2 x y + 4 x^{2} y^{2} c x + 4 x^{2} y^{2} \cdot 2 c + 4 x c^{2} x^{2} y + 4 x c^{2} \cdot 2 x y + 4 x c^{2} c x + 4 x c^{2} \cdot 2 c + 8 c x^{2} y x^{2} y + 8 c x^{2} y \cdot 2 x y + 8 c x^{2} yc x + 8 c x^{2} y \cdot 2 c + 8 c x y x^{2} y + 8 c x y \cdot 2 x y + 8 c x yc x + 8 c x y \cdot 2 c : x^{6} y^{3} + c^{3} x^{3} + 6 x^{5} y^{3} + 3 c x^{5} y^{2} + 3 c^{2} x^{4} y + 2 c^{3} x^{2} + 12 x^{4} y^{3} + 8 c^{3} + 12 x c^{3} + 8 x^{3} y^{3} + 4 x^{2} c^{3} + 18 c x^{4} y^{2} + 14 c^{2} x^{3} y + 36 c x^{3} y^{2} + 28 c^{2} x^{2} y + 24 x c^{2} y + 24 c x^{2} y^{2} + 4 x^{3} c^{2} y + 8 x^{2} c^{2} y

= x^{6} y^{3} + c^{3} x^{3} + 6 x^{5} y^{3} + 3 c x^{5} y^{2} + 3 c^{2} x^{4} y + 2 c^{3} x^{2} + 12 x^{4} y^{3} + 8 c^{3} + 12 x c^{3} + 8 x^{3} y^{3} + 4 x^{2} c^{3} + 18 c x^{4} y^{2} + 14 c^{2} x^{3} y + 36 c x^{3} y^{2} + 28 c^{2} x^{2} y + 24 x c^{2} y + 24 c x^{2} y^{2} + 4 x^{3} c^{2} y + 8 x^{2} c^{2} y

(2 x - 5 y)^{3} - (2 x - y)^{3}

x^{2} - y^{2} + 25 + 10 x

3 a (a - b) - 2 a (a + b)

(3 x - 1)^{2} - 9 x - 7

sin^{4} (a) + sin^{2} (a) cos^{2} (a) - sin^{2} (a)

What is expand ((x^2*y)+((2*x)*y)+(c*x)+(2*c))^3 ?
The solution to expand ((x^2*y)+((2*x)*y)+(c*x)+(2*c))^3 is