What is expand (4+Δx)^3 ?

The solution to expand (4+Δx)^3 is 64+48Δx+12Δ^2x^2+Δ^3x^3

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expand (4+Δx)^3

expand

(4 + Δ x)^{3}

64 + 48Δ x + 12 Δ^{2} x^{2} + Δ^{3} x^{3}

Solution steps

(4 + Δ x)^{3}

Apply Perfect Cube Formula:

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

a = 4, b = Δ x

= 4^{3} + 3 \cdot 4^{2} Δ x + 3 \cdot 4 (Δ x)^{2} + (Δ x)^{3}

Simplify

4^{3} + 3 \cdot 4^{2} Δ x + 3 \cdot 4 (Δ x)^{2} + (Δ x)^{3} : 64 + 48Δ x + 12 Δ^{2} x^{2} + Δ^{3} x^{3}

= 64 + 48Δ x + 12 Δ^{2} x^{2} + Δ^{3} x^{3}

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What is expand (4+Δx)^3 ?
The solution to expand (4+Δx)^3 is 64+48Δx+12Δ^2x^2+Δ^3x^3