Polynomials and fractions

9000146206

Level: 
A
Factor the following expression. \[ x^{2}y^{10} - 81 \]
\(\left (xy^{5} - 9\right )\left (xy^{5} + 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{5} - 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{2} + 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{2} - 9\right )\)

9000146205

Level: 
A
Factor the following expression. \[ 9a^{6} - 4b^{2} \]
\(\left (3a^{3} - 2b\right )\left (3a^{3} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{3} - 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} - 2b\right )\)

9000146208

Level: 
B
Factor the following expression. \[ \left (2x - 1\right )^{2} -\left (x + 3\right )^{2} \]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)

9000146209

Level: 
C
Factor the following expression. \[ 27a^{3} - 8b^{9} \]
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 6ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 6ab^{3} + 4b^{6}\right )\)
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 12ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 12ab^{3} + 4b^{6}\right )\)

9000101710

Level: 
B
Factor the following polynomial. \[ x^{2}y - x^{2}z - 4xyz + 4xy^{2} + 4y^{3} - 4y^{2}z \]
\(\left (y - z\right )\left (x + 2y\right )^{2}\)
\(\left (y - z\right )\left (x - 2y\right )^{2}\)
\(\left (y - z\right )\left (x^{2} + 4y + 4y^{2}\right )\)
\(\left (y + z\right )\left (x - 2y\right )^{2}\)

9000101704

Level: 
B
Factor the following polynomial. \[ 16x^{2}y^{4} - 25x^{4}y^{2} \]
\(\left (4xy^{2} - 5x^{2}y\right )\left (4xy^{2} + 5x^{2}y\right )\)
\(\left (4xy - 5x^{2}y\right )\left (4xy^{2} + 5xy\right )\)
\(\left (4x^{2}y^{2} - 5xy\right )\left (4x^{2}y^{2} + 5xy\right )\)
\(\left (4xy^{2} - 5x^{2}y\right )^{2}\)