9000101706 Level: BFactor the following polynomial. \[ 8x^{4} - 48x^{3} + 72x^{2} \]\(8x^{2}\left (x - 3\right )^{2}\)\(- 8x^{2}\left (3 - x\right )^{2}\)\(8\left (x^{2} - 3\right )^{2}\)\(8x\left (x^{2} - 3\right )^{2}\)
9000101710 Level: BFactor the following polynomial. \[ x^{2}y - x^{2}z - 4xyz + 4xy^{2} + 4y^{3} - 4y^{2}z \]\(\left (y - z\right )\left (x + 2y\right )^{2}\)\(\left (y - z\right )\left (x - 2y\right )^{2}\)\(\left (y - z\right )\left (x^{2} + 4y + 4y^{2}\right )\)\(\left (y + z\right )\left (x - 2y\right )^{2}\)
9000146201 Level: BExpand the following expression. \[ \left (2x^{3} - y^{2}\right )^{3} \]\(8x^{9} - 12x^{6}y^{2} + 6x^{3}y^{4} - y^{6}\)\(8x^{9} - 4x^{6}y^{2} + 2x^{3}y^{4} - y^{6}\)\(8x^{6} - 12x^{5}y^{2} + 6x^{3}y^{4} - y^{5}\)\(8x^{6} - 4x^{5}y^{2} + 2x^{3}y^{4} - y^{5}\)
9000146202 Level: BExpand the following expression. \[ \left (a^{2} + \sqrt{3}b\right )^{3} \]\(a^{6} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)\(a^{6} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)\(a^{5} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)\(a^{5} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
9000146207 Level: BFactor the following expression. \[ 4a^{2} -\left (a - 1\right )^{2} \]\(\left (a + 1\right )\left (3a - 1\right )\)\(\left (a - 1\right )\left (3a - 1\right )\)\(\left (a + 1\right )\left (3a + 1\right )\)\(\left (a - 1\right )\left (3a + 1\right )\)
9000146208 Level: BFactor the following expression. \[ \left (2x - 1\right )^{2} -\left (x + 3\right )^{2} \]\(\left (x - 4\right )\left (3x + 2\right )\)\(\left (x - 4\right )\left (3x - 2\right )\)\(\left (x + 4\right )\left (3x + 2\right )\)\(\left (x + 4\right )\left (3x - 2\right )\)
1003032402 Level: CThe polynomial \( 27+x^3 \) is equal to a product:\( (3+x)\left(9-3x+x^2\right) \)\( (3+x)^2(3-x) \)\( (3-x)\left(9+3x+x^2\right) \)\( (3+x)^3 \)
1003032403 Level: CReducing the rational expression \( \frac{4m^2-4mn+n^2}{8m^3-n^3} \) we get:\( \frac{2m-n}{4m^2+2mn+n^2} \)\( \frac{m-4mn+1}{2m-n} \)\( \frac{2m-n}{4m^2-4mn+n^2} \)\( \frac{2m-n}{4m^2+4mn+n^2} \)
1003032404 Level: CSimplifying the rational expression \( \frac{x^6-y^6}{x^2-y^2} \) we get:\( \left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right) \)\( x^4-y^4 \)\( x^3 - y^3 \)\( \left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right) \)
1003032502 Level: CLet the polynomial \( (x-2)^5-(x+2)^5 \) be expressed in the form \( a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \). Give the sum of \( a_5+a_4+a_3+a_2+a_1 \).\( -180 \)\( -244 \)\( -242 \)\( -212 \)