What is expand (x-Δx)^3 ?

The solution to expand (x-Δx)^3 is x^3-3Δx^3+3Δ^2x^3-Δ^3x^3

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expand (x-Δx)^3

expand

(x - Δ x)^{3}

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

Solution steps

(x - Δ x)^{3}

Apply Perfect Cube Formula:

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

a = x, b = Δ x

= x^{3} - 3 x^{2} Δ x + 3 x (Δ x)^{2} - (Δ x)^{3}

Simplify

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

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

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

(2 A x + B) e^{x} + e^{x} (A x^{2} + B x)

\frac{( 6 - x ) ^{2}}{9}

a (arctan (wT) - arctan (w Y))

a^{2} b^{2} - c^{2} d^{2} (sin (2 α) + 1)

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