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}

(1 + 2 i)^{4}

(x + Δ x)^{2}

(2 - i)^{4}

(1 + cos (x))^{2}

(x - i y)^{2}

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