What is expand (y+Δy)^3 ?

The solution to expand (y+Δy)^3 is y^3+3Δy^3+3Δ^2y^3+Δ^3y^3

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expand (y+Δy)^3

expand

(y + Δ y)^{3}

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

Solution steps

(y + Δ y)^{3}

Apply Perfect Cube Formula:

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

a = y, b = Δ y

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

Simplify

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

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

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What is expand (y+Δy)^3 ?
The solution to expand (y+Δy)^3 is y^3+3Δy^3+3Δ^2y^3+Δ^3y^3