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

The solution to expand x(x-1)^2(x+2)^3(x+3) is x^7+7x^6+13x^5-7x^4-34x^3-4x^2+24x

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

expand

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

x^{7} + 7 x^{6} + 13 x^{5} - 7 x^{4} - 34 x^{3} - 4 x^{2} + 24 x

Solution steps

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

Expand

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

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

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

Expand

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

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

Expand

x (x + 3) : x^{2} + 3 x

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

Expand

(x^{2} + 3 x) (x^{3} + 6 x^{2} + 12 x + 8) : x^{5} + 9 x^{4} + 30 x^{3} + 44 x^{2} + 24 x

= (x^{5} + 9 x^{4} + 30 x^{3} + 44 x^{2} + 24 x) (x^{2} - 2 x + 1)

Distribute parentheses

= x^{5} x^{2} + x^{5} (- 2 x) + x^{5} \cdot 1 + 9 x^{4} x^{2} + 9 x^{4} (- 2 x) + 9 x^{4} \cdot 1 + 30 x^{3} x^{2} + 30 x^{3} (- 2 x) + 30 x^{3} \cdot 1 + 44 x^{2} x^{2} + 44 x^{2} (- 2 x) + 44 x^{2} \cdot 1 + 24 x x^{2} + 24 x (- 2 x) + 24 x \cdot 1

Simplify

x^{5} x^{2} + x^{5} (- 2 x) + x^{5} \cdot 1 + 9 x^{4} x^{2} + 9 x^{4} (- 2 x) + 9 x^{4} \cdot 1 + 30 x^{3} x^{2} + 30 x^{3} (- 2 x) + 30 x^{3} \cdot 1 + 44 x^{2} x^{2} + 44 x^{2} (- 2 x) + 44 x^{2} \cdot 1 + 24 x x^{2} + 24 x (- 2 x) + 24 x \cdot 1 : x^{7} + 7 x^{6} + 13 x^{5} - 7 x^{4} - 34 x^{3} - 4 x^{2} + 24 x

= x^{7} + 7 x^{6} + 13 x^{5} - 7 x^{4} - 34 x^{3} - 4 x^{2} + 24 x

\frac{125 x y ^{6}}{5 x ^{7} y ^{5}}

7 \frac{3}{5}

\frac{6 x ^{3} y ^{4} z ^{2}}{3 x ^{2} y ^{2} z ^{2}}

0.2 (- 61)^{2}

\frac{2 - \frac{4}{x + 2}}{5 - \frac{10}{x + 2}}

What is expand x(x-1)^2(x+2)^3(x+3) ?
The solution to expand x(x-1)^2(x+2)^3(x+3) is x^7+7x^6+13x^5-7x^4-34x^3-4x^2+24x