What is expand e^{x-5}(x-1)^2 ?

The solution to expand e^{x-5}(x-1)^2 is e^{x-5}x^2-2e^{x-5}x+e^{x-5}

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expand e^{x-5}(x-1)^2

expand

e^{x - 5} (x - 1)^{2}

e^{x - 5} x^{2} - 2 e^{x - 5} x + e^{x - 5}

Solution steps

e^{x - 5} (x - 1)^{2}

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

= e^{x - 5} (x^{2} - 2 x + 1)

Distribute parentheses

= e^{x - 5} x^{2} + e^{x - 5} (- 2 x) + e^{x - 5} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= e^{x - 5} x^{2} - 2 e^{x - 5} x + 1 \cdot e^{x - 5}

Multiply:

1 \cdot e^{x - 5} = e^{x - 5}

= e^{x - 5} x^{2} - 2 e^{x - 5} x + e^{x - 5}

2 (x + \frac{1}{4})

(- 6 e^{- 5 x} x - \frac{11 e ^{- 5 x}}{5}) x e^{5 x}

cos (π (t - 1)) + sin (π (t - 1))

(1 + \frac{5 i}{n})^{2}

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

What is expand e^{x-5}(x-1)^2 ?
The solution to expand e^{x-5}(x-1)^2 is e^{x-5}x^2-2e^{x-5}x+e^{x-5}