Algebraic Expressions and Polynomials

Benjamin is designing a garden and needs to calculate the area of a specific section. He uses the expression \((-4m^2n^3) \cdot \frac{1}{6} m^{10}n^{-4}\) to determine the area. Simplify the expression to find the area in standard form.

• -\frac{2}{3}m^{12}n^{-1}

• -\frac{2}{3}m^{8}n^{-1}

• -\frac{2}{3}m^{12}n^{7}

• -\frac{2}{3}m^{8}n^{7}

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the expression: \((8a^2 - 6 - 8a) + (1 - 6a - 7a^2)\). Final answers should be written in standard form.

• -a^2 - 8a - 5

• a^2 - 8a - 5

• -a^2 + 8a + 5

• a^2 + 8a + 5

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

Simplify the expression: \((6x - 7x^2 + 7) - (5x^2 + 2x - 2x^3 - 1)\). Final answers should be written in standard form.

• -2x^3 - 12x^2 + 4x + 8

• -2x^3 - 12x^2 + 4x + 6

• -2x^3 - 12x^2 + 4x + 7

• -2x^3 - 12x^2 + 4x + 5

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the expression: \((y + 4)^3 - 2y(y - 1)\). Final answers should be written in standard form.

• y^3 + 12y^2 + 48y + 64 - 2y^2 + 2y

• y^3 + 10y^2 + 50y + 64

• y^3 + 12y^2 + 46y + 64

• y^3 + 10y^2 + 46y + 64

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the expression: \((3k - 6)(k^2 - k + 7)\). Final answers should be written in standard form.

• 3k^3 - 3k^2 + 21k - 6k^2 + 6k - 42

• 3k^3 - 9k^2 + 21k - 6k^2 + 6k - 42

• 3k^3 - 9k^2 + 21k - 6k^2 + 12k - 42

• 3k^3 - 9k^2 + 21k - 6k^2 + 6k - 42

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the expression: \(\frac{-8c^6d^4 + 56c^4d^2 - 24c^2d}{8c^2d}\). Final answers should be written in standard form.

• -c^4d^3 + 7c^2d - 3

• -c^4d^3 + 7c^2d + 3

• c^4d^3 - 7c^2d + 3

• c^4d^3 + 7c^2d - 3

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Factor the polynomial completely: \(9x^3 + 21x^2\).

• 3x^2(3x + 7)

• 9x(x^2 + 21)

• x(9x^2 + 21x)

• 3x(3x^2 + 7x)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor the polynomial completely: \(3n^4 - 147\).

• \(3(n^2 - 7)(n^2 + 7)\)

• \(3(n^2 - 49)\)

• \(3(n^2 + 49)\)

• \(3(n^2 - 7)^2\)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

Factor the polynomial completely: \(64a^3 - 343b^3\).

• \((4a - 7b)(16a^2 + 28ab + 49b^2)\)

• \((8a - 7b)(8a^2 + 14ab + 49b^2)\)

• \((4a + 7b)(16a^2 - 28ab + 49b^2)\)

• \((8a + 7b)(8a^2 - 14ab + 49b^2)\)

Tags

CCSS.HSA.APR.A.1

Factor the polynomial completely: \(648w + 1029w^4\).

• \(3w(216 + 343w^3)\)

• \(9w(72 + 114w^3)\)

• \(27w(24 + 38w^3)\)

• \(81w(8 + 13w^3)\)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2