What is expand ((x+Δx)-1)(x-1) ?

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

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expand ((x+Δx)-1)(x-1)

expand

((x + Δ x) - 1) (x - 1)

Δ x^{2} + x^{2} - Δ x - 2 x + 1

Solution steps

((x + Δ x) - 1) (x - 1)

Apply FOIL method:

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

a = (x + Δ x), b = - 1, c = x, d = - 1

= (x + Δ x) x + (x + Δ x) (- 1) + (- 1) x + (- 1) (- 1)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

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

Simplify

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

= Δ x^{2} + x^{2} - Δ x - 2 x + 1

a ((a - b) \cdot (a + 2 b))

\frac{y ( y + 1 ) ^{2}}{2}

- \frac{1}{( - s - 1 ) ^{2}}

\frac{x ^{2} - x - 8}{( x + 3 ) ( 4 - x )}

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

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