What is expand (x-1)(e^Tx-1) ?

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

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expand (x-1)(e^Tx-1)

expand

(x - 1) (e^{T} x - 1)

e^{T} x^{2} - x - e^{T} x + 1

Solution steps

(x - 1) (e^{T} x - 1)

Apply FOIL method:

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

a = x, b = - 1, c = e^{T} x, d = - 1

= x e^{T} x + x (- 1) + (- 1) e^{T} x + (- 1) (- 1)

Apply minus-plus rules

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

= e^{T} xx - 1 \cdot x - 1 \cdot e^{T} x + 1 \cdot 1

Simplify

e^{T} xx - 1 \cdot x - 1 \cdot e^{T} x + 1 \cdot 1 : e^{T} x^{2} - x - e^{T} x + 1

= e^{T} x^{2} - x - e^{T} x + 1

- \frac{4 ( x ^{2} + 4 x + 2 )}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

α^{2} β^{2} (α β + α + β + 1)^{2}

(x^{2} - 4) d x

\frac{d}{d x} ((0) (12 x^{3} - 24 x))

(x - a^{2} + 2 a - 3) (x - b^{2} + 2 b - 3) (x - c^{2} + 2 c - 3)

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