What is expand 2[(x+Δx)^2+1] ?

The solution to expand 2[(x+Δx)^2+1] is 2x^2+4Δx^2+2Δ^2x^2+2

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expand 2[(x+Δx)^2+1]

expand

2 [(x + Δ x)^{2} + 1]

2 x^{2} + 4Δ x^{2} + 2 Δ^{2} x^{2} + 2

Solution steps

2 ((x + Δ x)^{2} + 1)

Expand

(x + Δ x)^{2} + 1 : x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + 1

= 2 (x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + 1)

Distribute parentheses

= 2 x^{2} + 2 \cdot 2Δ x^{2} + 2 Δ^{2} x^{2} + 2 \cdot 1

Simplify

2 x^{2} + 2 \cdot 2Δ x^{2} + 2 Δ^{2} x^{2} + 2 \cdot 1 : 2 x^{2} + 4Δ x^{2} + 2 Δ^{2} x^{2} + 2

= 2 x^{2} + 4Δ x^{2} + 2 Δ^{2} x^{2} + 2

- \frac{7}{( x + 2 ) ( x - 5 )}

\frac{d ^{2}}{d t ^{2}} (x (t, α)) + ω^{2} (a cos (ω) t + α)

l im x \Rightarrow - 2 (x^{2} - x - 64 - 2 x)

\frac{d}{d t} ((r (t)) (t + t^{3} - t^{2}))

(\frac{6 x}{( 5000 + x ) ^{2}})^{'} \cdot (5000 + x)

What is expand 2[(x+Δx)^2+1] ?
The solution to expand 2[(x+Δx)^2+1] is 2x^2+4Δx^2+2Δ^2x^2+2