Polynomials and fractions

2010004401

Level:

From the given expressions choose the one, that by substituting for

*

into a trinomial

25 x^{4} y^{2} + * + 4

makes possible to express the trinomial as a square of a sum, i.e.

(A + B)^{2}

20 x^{2} y

10 x^{2} y

100 x^{2} y

40 x^{2} y

2010004402

Level:

From the given expressions choose the one, that by substituting for

*

into a trinomial

9 - * + 16 a^{2} b^{4}

makes possible to express the trinomial as a square of a difference, i.e.

(A - B)^{2}

24 a b^{2}

12 a b^{2}

144 a b^{2}

48 a b^{2}

2010004405

Level:

Factor the expression:

3 x y - t y - 12 x z + 4 t z

(3 x - t) (y - 4 z)

(t - 3 x) (y - 4 z)

(3 x - t) (4 z - y)

(t - 3 x) (y + 4 z)

2010004406

Level:

Factor the expression:

5 a b - a c + 15 b d - 3 c d

(5 b - c) (a + 3 d)

(c - 5 b) (a + 3 d)

(5 b - c) (a - 3 d)

(c - 5 b) (a - 3 d)

2010006601

Level:

Simplify the expression:

\frac{a + 1}{2} - \frac{b - 1}{3} - \frac{a - b - 1}{4} + \frac{b - a - 1}{6} - \frac{3 b - a + 1}{12}

\frac{a - b + 5}{6}

\frac{- 4 b - 1}{6}

\frac{5}{6}

0

2010006602

Level:

Simplify the expression:

\frac{a - 1}{2} + \frac{b + 1}{3} - \frac{a + b - 1}{6} - \frac{b - a + 1}{9} - \frac{b - 4 a}{18}

\frac{6 a - 1}{9}

\frac{2 a + 3 b - 2}{9}

- \frac{1}{9}

0

2010008801

Level:

Simplify:

4 (2 p^{4} - 5 p^{3} q + 2 p^{2} q^{2} - 6 p q^{3}) - 2 (3 p^{4} - 8 p^{3} q + 5 p^{2} q^{2} - p q^{3})

2 p (p^{3} - 2 p^{2} q - p q^{2} - 11 q^{3})

2 p (p^{3} - 18 p^{2} q + 9 p q^{2} - 13 q^{3})

2 p (p^{3} - 18 p^{2} q - p q^{2} - 11 q^{3})

2 p (p^{3} - 2 p^{2} q + 9 p q^{2} - 13 q^{3})

2010008802

Level:

Simplify:

2 (3 r^{4} - 8 r^{3} s - 5 r^{2} s^{2} + r s^{3}) - 4 (2 r^{4} - 5 r^{3} s + 2 r^{2} s^{2} - 6 r s^{3})

- 2 r (r^{3} - 2 r^{2} s + 9 r s^{2} - 13 s^{3})

- 2 r (r^{3} + 18 r^{2} s + r s^{2} + 11 s^{3})

- 2 r (r^{3} - 2 r^{2} s + 9 r s^{2} + 11 s^{3})

- 2 r (r^{3} + 18 r^{2} s + r s^{2} - 13 s^{3})

2010008803

Level:

Simplify:

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

x^{3}

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

x^{3} - 4 x y^{2}

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

2010008804

Level:

Simplify:

r s (2 r - s) - {r^{3} - [s^{2} (r - 3 s) - r^{2} (2 s - r)]}

- 3 s^{3}

3 s^{3} - 2 r^{3}

3 s^{3}

3 s^{3} - 2 r^{3} + 4 r^{2} s

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Polynomials and fractions

2010004401

2010004402

2010004405

2010004406

2010006601

2010006602

2010008801

2010008802

2010008803

2010008804

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