9000146701
Level:
A
Expand the following polynomial.
\[
2 - (2x + 1) + x(5 - 2x) - 3(x - 2)
\]
\(- 2x^{2} + 7\)
\(- 2x^{2} + 9\)
\(- 2x^{2} - 3\)
\(- 2x^{2} - 5\)
Polynomials and Rational Expressions
9000146702
Level:
A
Expand the following expression.
\[
a - 4(2 - a) - a(5a + 1) + 2a(3 - 2a)
\]
\(- 9a^{2} + 10a - 8\)
\(- 9a^{2} + 12a - 8\)
\(- 9a^{2} + 2a - 8\)
\(- 9a^{2} + 4a - 8\)
9000146201
Level:
B
Expand 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:
B
Expand the following expression.
\[
\left (a^{2} + \sqrt{3}b\right )^{3}
\]
\(a^{6} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{6} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
9000146203
Level:
A
Expand the following expression.
\[
\left (x^{5} -\sqrt{2}y\right )^{2}
\]
\(x^{10} - 2\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} - 2\sqrt{2}x^{5}y - 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y - 2y^{2}\)
9000146204
Level:
A
Expand the following expression.
\[
\left (\frac{a}
{2} + 4b^{3}\right )^{2}
\]
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{5}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{5}\)
9000101601
Level:
A
Expand \((1 + x)\left (x^{2} + x - 1\right )(1 - x)\).
\(- x^{4} - x^{3} + 2x^{2} + x - 1\)
\(x^{4} - x^{3} + 2x^{2} + x + 1\)
\(- x^{4} + x^{3} - 1\)
\(x^{4} + x^{3} - 2x^{2} + x - 1\)
9000101604
Level:
A
Expand the polynomial \(\left (2x^{2} + 4x\right )^{2} -\left (4x - 2x^{2}\right )^{2}\).
\(32x^{3}\)
\(0\)
\(32x^{3} - 8x\)
\(32x^{3} - 32x^{2} + 8x\)
9000101602
Level:
A
Simplify the polynomial \((x - 1)(x + 1)\left (x^{2} + 1\right ) -\left (x^{2} - 1\right )^{2}\)
into one of the following forms.
\(2\left (x^{2} - 1\right )\)
\(0\)
\(2\left (x^{2} - 1\right )(x + 1)\)
\(x^{2} - 1\)
9000101606
Level:
B
Expand \(\left (x - y\right )^{3} - x\left (x + y\right )^{2}\).
\(- y^{3} - 5x^{2}y + 2xy^{2}\)
\(y^{3} - 5x^{2}y + 2xy^{2}\)
\(- y^{3} - 5x^{2}y - 4xy^{2}\)
\(- y^{3} - 5x^{2}y + 4xy^{2}\)