What is expand ((x+Δx)^2-2)^2 ?

The solution to expand ((x+Δx)^2-2)^2 is Δ^4x^4+4Δ^3x^4+6Δ^2x^4+4Δx^4+x^4-4Δ^2x^2-8Δx^2-4x^2+4

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expand ((x+Δx)^2-2)^2

expand

((x + Δ x)^{2} - 2)^{2}

Δ^{4} x^{4} + 4 Δ^{3} x^{4} + 6 Δ^{2} x^{4} + 4Δ x^{4} + x^{4} - 4 Δ^{2} x^{2} - 8Δ x^{2} - 4 x^{2} + 4

Solution steps

((x + Δ x)^{2} - 2)^{2}

Expand

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

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

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

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

Expand

(x^{2} + 2Δ x^{2} + Δ^{2} x^{2} - 2) (x^{2} + 2Δ x^{2} + Δ^{2} x^{2} - 2) : Δ^{4} x^{4} + 4 Δ^{3} x^{4} + 6 Δ^{2} x^{4} + 4Δ x^{4} + x^{4} - 4 Δ^{2} x^{2} - 8Δ x^{2} - 4 x^{2} + 4

= Δ^{4} x^{4} + 4 Δ^{3} x^{4} + 6 Δ^{2} x^{4} + 4Δ x^{4} + x^{4} - 4 Δ^{2} x^{2} - 8Δ x^{2} - 4 x^{2} + 4

x^{2} + y^{2} (x^{2} + y^{2})

(- cos (x) - sin (x)) (- sin (x) + cos (x) + 2)

(3 x y^{2} - 4 y) + (3 x - 4 x^{2} y) y^{'} (x)

(x - 4) (x - \frac{2}{3})

\frac{d ^{2}}{d x ^{2}} ((y) (- 5 x^{2} + 5 x))

What is expand ((x+Δx)^2-2)^2 ?
The solution to expand ((x+Δx)^2-2)^2 is Δ^4x^4+4Δ^3x^4+6Δ^2x^4+4Δx^4+x^4-4Δ^2x^2-8Δx^2-4x^2+4