What is expand (x+Δx)((x+Δx)+1) ?

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

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expand (x+Δx)((x+Δx)+1)

expand

(x + Δ x) ((x + Δ x) + 1)

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

Solution steps

(x + Δ x) ((x + Δ x) + 1)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = x, b = Δ x, c = (x + Δ x), d = 1

= x (x + Δ x) + x \cdot 1 + Δ x (x + Δ x) + Δ x \cdot 1

= x (x + Δ x) + 1 \cdot x + Δ x (x + Δ x) + 1Δ x

Simplify

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

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

\frac{( x - 1 ) ( x ^{2} - 4 x + 5 )}{x}

\frac{1}{x \cdot ( x - 118 )}

A (6, - 3) B (- 8, - 5)

r x (r x - 1) k e^{r x - 2}

(x^{3} + 7) e^{2}

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