What is expand (x-1)^2*e^{x-4} ?

The solution to expand (x-1)^2*e^{x-4} is e^{x-4}x^2-2e^{x-4}x+e^{x-4}

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expand (x-1)^2*e^{x-4}

expand

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

e^{x - 4} x^{2} - 2 e^{x - 4} x + e^{x - 4}

Solution steps

(x - 1)^{2} e^{x - 4}

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= e^{x - 4} x^{2} - 2 e^{x - 4} x + 1 \cdot e^{x - 4}

Multiply:

1 \cdot e^{x - 4} = e^{x - 4}

= e^{x - 4} x^{2} - 2 e^{x - 4} x + e^{x - 4}

2 x \cdot x^{3}

\frac{( x - 4 ) ( x - 5 )}{( x - 3 ) ^{2} ( x ^{2} + 2 x + 1 )}

\frac{d}{d z} ((z) (x y^{7} - x^{2} y))

\frac{6 x + 7}{( 15 x + 5 ) ( x - 9 ) ^{'}}

\frac{\partial}{\partial x} ((z) ((x + 2 y)^{2}))

What is expand (x-1)^2*e^{x-4} ?
The solution to expand (x-1)^2*e^{x-4} is e^{x-4}x^2-2e^{x-4}x+e^{x-4}