Polynomials and fractions

1003032401

Level:

Factoring the polynomial

625 x^{4} - 1

we get:

(25 x^{2} + 1) (5 x - 1) (5 x + 1)

(5 x - 1) (5 x + 1)^{2}

(5 x - 1)^{4}

(25 x^{2} + 1) (5 x - 1)^{2}

1003032501

Level:

The product

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

equals:

x^{6} + x^{5} y + x^{4} y^{2} + 2 x^{3} y^{3} + x^{2} y^{4} + x y^{5} + y^{6}

x^{6} - x^{5} y + x^{4} y^{2} - 2 x^{3} y^{3} + x^{2} y^{4} - x y^{5} + y^{6}

(x + y)^{6}

x^{6} + y^{6}

1003032504

Level:

Factoring the polynomial

- 4 x^{4} + 26 x^{3} - 12 x^{2}

you get:

- 2 x^{2} (x - 6) (2 x - 1)

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

- 2 x^{2} (x + 6) (2 x + 1)

2 x^{2} (x - 6) (2 x + 1)

2010000814

Level:

Assuming

x \neq 0

y \neq 0

y \neq \pm 1

, simplify the expression:

[{(\frac{y - 1}{y})}^{2} : {(\frac{x}{y + 1})}^{2}] : \frac{2 (y^{2} - 1)}{x y}

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

2

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

\frac{y - 1}{2}

2010000901

Level:

Assuming

x y \neq 1

, simplify the expression:

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

y

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

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

y (1 + x^{2})

2010000902

Level:

Assuming

x \neq \pm y

and

x \neq 0

, simplify the expression:

(\frac{y}{y - x} - \frac{2 x}{y + x} - \frac{y^{2}}{y^{2} - x^{2}}) : (\frac{1}{x + y} - \frac{y}{y^{2} - x^{2}})

y - 2 x

2 x - y

\frac{2 x - y}{x}

0

Suppose we are given the following equality of two fractions with nonzero denominators. From the given expressions, choose the one that by substituting to the starred position makes the equality true.

\frac{2 - 3 x}{x + 2} = \frac{2 (9 x^{2} - 12 x + 4)}{*}

(2 x + 4) (2 - 3 x)

(x + 2) (2 - 3 x)

(x + 2) (4 - 9 x)

(2 x + 4) (3 x - 2)

2010001303

Level:

Expand

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

x^{3} + 2 x^{2} y + 5 x y^{2}

x^{3} + 2 x^{2} y + x y^{2}

x^{3} + 2 x^{2} y + x y^{2} + 2 y^{3}

x^{3} + 2 x^{2} y + 5 x y^{2} + 2 y^{3}

2010001304

Level:

Factor the following polynomial.

20 x y + 12 y - 5 x - 3

(4 y - 1) (5 x + 3)

4 y (5 x + 3)

(1 - 4 y) (5 x + 3)

- 4 y (5 x + 3)

2010001305

Level:

Factor the following polynomial expression.

36 b^{2} c^{2} - 9 a^{2} b^{2} - 36 c^{2} d^{2} + 9 a^{2} d^{2}

9 (b - d) (b + d) (2 c + a) (2 c - a)

(b^{2} + d^{2}) (36 c^{2} + 9 a^{2})

9 (a - d) (a + d) (2 b + c) (2 b - c)

(a^{2} + d^{2}) (36 b^{2} + 9 c^{2})

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Polynomials and fractions

1003032401

1003032501

1003032504

2010000814

2010000901

2010000902

2010000905

2010001303

2010001304

2010001305

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