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

The solution to expand (x-2)^2(x-3)^3 is x^5-13x^4+67x^3-171x^2+216x-108

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

expand

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

x^{5} - 13 x^{4} + 67 x^{3} - 171 x^{2} + 216 x - 108

Solution steps

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

Expand

(x - 2)^{2} : x^{2} - 4 x + 4

= (x^{2} - 4 x + 4) (x - 3)^{3}

= (x - 3)^{3} (x^{2} - 4 x + 4)

Expand

(x - 3)^{3} : x^{3} - 9 x^{2} + 27 x - 27

= (x^{3} - 9 x^{2} + 27 x - 27) (x^{2} - 4 x + 4)

Distribute parentheses

= x^{3} x^{2} + x^{3} (- 4 x) + x^{3} \cdot 4 - 9 x^{2} x^{2} - 9 x^{2} (- 4 x) - 9 x^{2} \cdot 4 + 27 x x^{2} + 27 x (- 4 x) + 27 x \cdot 4 - 27 x^{2} - 27 (- 4 x) - 27 \cdot 4

Simplify

x^{3} x^{2} + x^{3} (- 4 x) + x^{3} \cdot 4 - 9 x^{2} x^{2} - 9 x^{2} (- 4 x) - 9 x^{2} \cdot 4 + 27 x x^{2} + 27 x (- 4 x) + 27 x \cdot 4 - 27 x^{2} - 27 (- 4 x) - 27 \cdot 4 : x^{5} - 13 x^{4} + 67 x^{3} - 171 x^{2} + 216 x - 108

= x^{5} - 13 x^{4} + 67 x^{3} - 171 x^{2} + 216 x - 108

\int_{0}^{\infty} \frac{x}{x ^{3}} d x

(5 x^{6} + 2 x^{3})^{4}

f (x) = x e^{x} csc (x)

\int 9 e^{\frac{x}{4}} d x

\int_{- \infty}^{0} x e^{- x} d x

What is expand (x-2)^2(x-3)^3 ?
The solution to expand (x-2)^2(x-3)^3 is x^5-13x^4+67x^3-171x^2+216x-108