Polynomials and fractions

2000006102

Level:

Simplify:

2 (4 y^{2} - 2 y + 5) + 2 y^{2} - (3 y^{2} + 5 y - 1)

7 y^{2} - 9 y + 11

7 y^{2} + y + 11

7 y^{2} - 9 y + 9

7 y^{2} + y + 9

2010000801

Level:

The product

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

equals:

3 x^{3} y - 5 x^{2} y^{2} + 2 x y^{3} + 12 x^{2} y - 8 x y^{2}

3 x^{3} y + x^{2} y^{2} + 2 x y^{3} + 12 x^{2} y - 8 x y^{2}

3 x^{3} y - 5 x^{2} y^{2} + 2 x y^{3} - 12 x^{2} y - 8 x y^{2}

3 x^{3} y - x^{2} y^{2} + 2 x y^{3} + 12 x^{2} y - 8 x y^{2}

2010000807

Level:

Assuming

x \neq 0

y \neq 0

x \neq - y

, simplify the following expression.

\frac{\frac{1}{y^{2}} - \frac{1}{x^{2}}}{- \frac{1}{x} - \frac{1}{y}}

\frac{y - x}{x y}

\frac{x - y}{x y}

x - y

y - x

2010000808

Level:

Assuming

x \notin {0; 1; 3}

, simplify the following expression.

\frac{x^{2} - 9}{x^{2} - x} : \frac{x^{2} - 3 x}{x - 1}

\frac{x + 3}{x^{2}}

\frac{x - 3}{x^{2}}

\frac{x + 3}{2 x}

\frac{x + 3}{x}

2010000809

Level:

Assuming

x \notin {- 4; 0; 3; 4}

, simplify the following expression.

\frac{x^{2} - 3 x}{x^{2} - 16} : \frac{x - 3}{x^{2} + 4 x}

\frac{x^{2}}{x - 4}

\frac{x - 4}{x^{2}}

\frac{x - 4}{x}

\frac{x}{x - 4}

2010000810

Level:

Evaluate the following expression at

x = 4

\frac{\frac{1}{\sqrt{x}}}{\frac{1}{x^{2}} - \frac{1}{x}}

- \frac{8}{3}

\frac{31}{3}

\frac{8}{3}

6

2010000811

Level:

Evaluate the following expression at

x = 9

\frac{\frac{1}{x} + \frac{1}{x^{2}}}{\frac{1}{\sqrt{x}}}

\frac{10}{27}

- \frac{10}{9}

- 30

30

2010000812

Level:

Assuming

y \neq 1

x \neq \pm y

, simplify the expression:

\frac{y^{2} - 2 x y + x^{2}}{(1 - y) (y - x)} \cdot \frac{3 y^{2} - 6 y + 3}{x^{2} - y^{2}}

\frac{3 (y - 1)}{x + y}

\frac{3 (1 - y)}{x + y}

\frac{3}{x + y}

3

2010001301

Level:

Expand

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

x^{4} - x^{3} + x - 1

x^{4} - x^{3} + 2 x^{2} + x - 1

x^{4} + x^{3} - x + 1

x^{4} + x^{3} - 2 x^{2} + x - 1

2010001302

Level:

Expand the polynomial

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

- 24 x^{3}

0

8 x^{2}

8 x^{2} - 24 x^{3}

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Polynomials and fractions

2000006102

2010000801

2010000807

2010000808

2010000809

2010000810

2010000811

2010000812

2010001301

2010001302

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