What is expand (x-y)^2((x-y)-Δ) ?

The solution to expand (x-y)^2((x-y)-Δ) is x^3-3x^2y+3xy^2-y^3-Δx^2+2Δxy-Δy^2

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expand (x-y)^2((x-y)-Δ)

expand

(x - y)^{2} ((x - y) - Δ)

x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

Solution steps

(x - y)^{2} ((x - y) - Δ)

Apply the distributive law:

a (b - c) = ab - a c

a = (x - y)^{2}, b = (x - y), c = Δ

= (x - y)^{2} (x - y) - (x - y)^{2} Δ

= (x - y)^{2} (x - y) - Δ (x - y)^{2}

Simplify

(x - y)^{2} (x - y) - Δ (x - y)^{2} : x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} v^{2}) d u

\frac{4 ( 3 ( 3 a + b ) - ( 5 a - b ) )}{12}

, (x - 1) (x - 2) (x - 4)

(p + Δ p + 1)^{2}

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

What is expand (x-y)^2((x-y)-Δ) ?
The solution to expand (x-y)^2((x-y)-Δ) is x^3-3x^2y+3xy^2-y^3-Δx^2+2Δxy-Δy^2