Polynomials and fractions

9000088808

Level:

Find the common denominator of the following three fractions. \[ \text{$ \frac{a} {a^{2}-ab}\ ,\qquad \frac{-b} {a^{2}-b^{2}} \ ,\qquad \frac{2b} {ab+b^{2}} $} \]

$ab(a^{2} - b^{2})$

$ab(a - b)$

$ab(a + b)$

$ab(a + b)^{2}$

9000101605

Level:

Expand $\left (4x^{2}y + 2xy^{2}\right )^{3}$.

$64x^{6}y^{3} + 96x^{5}y^{4} + 48x^{4}y^{5} + 8x^{3}y^{6}$

$16x^{2}y^{3} + 24x^{3}y^{3} + 8x^{3}y^{6}$

$64x^{6}y^{3} + 96x^{3}y^{3} + 96x^{4}y^{5} + 8x^{3}y^{6}$

$64x^{6}y^{3} + 8x^{3}y^{6}$

9000101606

Level:

Expand $\left (x - y\right )^{3} - x\left (x + y\right )^{2}$.

$- y^{3} - 5x^{2}y + 2xy^{2}$

$y^{3} - 5x^{2}y + 2xy^{2}$

$- y^{3} - 5x^{2}y - 4xy^{2}$

$- y^{3} - 5x^{2}y + 4xy^{2}$

9000101607

Level:

Expand $\left (x^{2} - y\right )^{3} -\left (y + x^{2}\right )^{3}$.

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

$- 2y^{3}$

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

$6x^{2}y - 2y^{3}$

9000101608

Level:

Expand $\left (3x + y\right )\left (9x^{2} - 3xy + y^{2}\right )$.

$27x^{3} + y^{3}$

$27x^{3} - y^{3}$

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

$27x^{3} + 3y^{3}$

9000101701

Level:

Factor the following polynomial. \[ 15xy - 10x - 3y + 2 \]

$\left (5x - 1\right )\left (3y - 2\right )$

$5x\left (3y - 2\right )$

$4x\left (3y - 2\right )$

$- 5x\left (3y - 2\right )$

9000101702

Level:

Factor the following polynomial. \[ 3x^{3} + 3x^{2}y + 4xy + 4y^{2} \]

$\left (3x^{2} + 4y\right )\left (x + y\right )$

$\left (3x + y\right )\left (x^{2} + y^{2}\right )$

$\left (3x^{2} + 4\right )\left (x + y^{2}\right )$

$\left (3x + y^{2}\right )\left (x + y\right )$

9000101703

Level:

Factor the following polynomial. \[ \left (5x - y\right )^{2} -\left (x - y\right )^{2} \]

$4x\left (6x - 2y\right )$

$x\left (5x - y\right )$

$6x\left (6x - 2y\right )$

$- 32x^{2}$

9000101704

Level:

Factor the following polynomial. \[ 16x^{2}y^{4} - 25x^{4}y^{2} \]

$\left (4xy^{2} - 5x^{2}y\right )\left (4xy^{2} + 5x^{2}y\right )$

$\left (4xy - 5x^{2}y\right )\left (4xy^{2} + 5xy\right )$

$\left (4x^{2}y^{2} - 5xy\right )\left (4x^{2}y^{2} + 5xy\right )$

$\left (4xy^{2} - 5x^{2}y\right )^{2}$

9000101705

Level:

Factor the following polynomial expression. \[ 16a^{2}b^{2} - 4a^{2}c^{2} - 16b^{2}d^{2} + 4c^{2}d^{2} \]

$4\left (a - d\right )\left (a + d\right )\left (2b + c\right )\left (2b - c\right )$

$4\left (a + b\right )^{2}\left (2b + c\right )^{2}$

$4\left (a - b\right )\left (a + b\right )\left (2b + c\right )\left (2b - c\right )$

$4\left (a - c\right )\left (a + c\right )\left (2b + d\right )\left (2b - d\right )$

Polynomials and fractions

9000088808

9000101605

9000101606

9000101607

9000101608

9000101701

9000101702

9000101703

9000101704

9000101705

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