What is expand (x+xΔ)^3 ?

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

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expand (x+xΔ)^3

expand

(x + x Δ)^{3}

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

Solution steps

(x + x Δ)^{3}

= (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 = x Δ

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

Simplify

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

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

(4 s - 2) e^{- \frac{π}{2} - s}

\frac{x}{( e ^{x} ( x + 2 ) )}

7 (x + Δ x)^{2} - 5 (x + Δ x)

\frac{( a + h ) ^{3}}{( a + h ) ^{2} + 1}

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