What is expand (x-2)^3(x-1) ?

The solution to expand (x-2)^3(x-1) is x^4-7x^3+18x^2-20x+8

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expand (x-2)^3(x-1)

expand

(x - 2)^{3} (x - 1)

x^{4} - 7 x^{3} + 18 x^{2} - 20 x + 8

Solution steps

(x - 2)^{3} (x - 1)

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

= (x^{3} - 6 x^{2} + 12 x - 8) (x - 1)

Distribute parentheses

= x^{3} x + x^{3} (- 1) - 6 x^{2} x - 6 x^{2} (- 1) + 12 xx + 12 x (- 1) - 8 x - 8 (- 1)

Simplify

x^{3} x + x^{3} (- 1) - 6 x^{2} x - 6 x^{2} (- 1) + 12 xx + 12 x (- 1) - 8 x - 8 (- 1) : x^{4} - 7 x^{3} + 18 x^{2} - 20 x + 8

= x^{4} - 7 x^{3} + 18 x^{2} - 20 x + 8

\frac{3 x ^{3} + 16 x ^{2} + 22 x + 4}{x + 2}

(5 m - 3) (m + 2)

\frac{x}{x ^{\frac{1}{4}}}

- 3 x^{3} - x

8 x + 36

What is expand (x-2)^3(x-1) ?
The solution to expand (x-2)^3(x-1) is x^4-7x^3+18x^2-20x+8