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Expanding Algebraic Expressions

Description: This quiz is designed to assess your understanding of expanding algebraic expressions. It covers various types of expressions, including binomials, trinomials, and polynomials. Each question presents an algebraic expression that needs to be expanded, and you are tasked with selecting the correct expanded form from the given options. Good luck!
Number of Questions: 14
Created by:
Tags: algebra expanding algebraic expressions binomials trinomials polynomials
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Expand the following expression: (2x + 3)(x - 4)

  1. 2x^2 - 5x - 12

  2. 2x^2 + 5x - 12

  3. 2x^2 - 8x - 12

  4. 2x^2 + 8x - 12

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (2x + 3)(x - 4) = 2x(x - 4) + 3(x - 4) = 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12.

Expand the following expression: (x^2 + 2x - 3)(x - 1)

  1. x^3 + x^2 - 5x - 3

  2. x^3 + x^2 - 5x + 3

  3. x^3 + x^2 + 5x - 3

  4. x^3 + x^2 + 5x + 3

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (x^2 + 2x - 3)(x - 1) = x^2(x - 1) + 2x(x - 1) - 3(x - 1) = x^3 - x^2 + 2x^2 - 2x - 3x + 3 = x^3 + x^2 - 5x - 3.

Expand the following expression: (2a - 3b)(4a + 5b)

  1. 8a^2 - 7ab - 15b^2

  2. 8a^2 + 7ab - 15b^2

  3. 8a^2 - 7ab + 15b^2

  4. 8a^2 + 7ab + 15b^2

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (2a - 3b)(4a + 5b) = 2a(4a + 5b) - 3b(4a + 5b) = 8a^2 + 10ab - 12ab - 15b^2 = 8a^2 - 7ab - 15b^2.

Expand the following expression: (x^3 - 2x^2 + 3x - 4)(x + 2)

  1. x^4 - x^3 - 4x^2 + 5x - 8

  2. x^4 - x^3 - 4x^2 + 5x + 8

  3. x^4 + x^3 - 4x^2 + 5x - 8

  4. x^4 + x^3 - 4x^2 + 5x + 8

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (x^3 - 2x^2 + 3x - 4)(x + 2) = x^3(x + 2) - 2x^2(x + 2) + 3x(x + 2) - 4(x + 2) = x^4 + 2x^3 - 2x^3 - 4x^2 + 3x^2 + 6x - 4x - 8 = x^4 - x^3 - 4x^2 + 5x - 8.

Expand the following expression: (a^2 + b^2)(a - b)

  1. a^3 - b^3

  2. a^3 + b^3

  3. a^2 - b^2

  4. a^2 + b^2

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (a^2 + b^2)(a - b) = a^2(a - b) + b^2(a - b) = a^3 - a^2b + a^2b - b^3 = a^3 - b^3.

Expand the following expression: (2x - 3y)^2

  1. 4x^2 - 9y^2

  2. 4x^2 + 9y^2

  3. 4x^2 - 12xy + 9y^2

  4. 4x^2 + 12xy + 9y^2

Show answer
Correct Option: C
Explanation:

To expand the expression, use the square of a binomial formula: (2x - 3y)^2 = (2x)^2 + 2(2x)(-3y) + (-3y)^2 = 4x^2 - 12xy + 9y^2.

Expand the following expression: (x + y + z)^3

  1. x^3 + y^3 + z^3 + 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz

  2. x^3 + y^3 + z^3 + 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) - 6xyz

  3. x^3 + y^3 + z^3 - 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz

  4. x^3 + y^3 + z^3 - 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) - 6xyz

Show answer
Correct Option: A
Explanation:

To expand the expression, use the cube of a binomial formula: (x + y + z)^3 = x^3 + 3x^2(y + z) + 3x(y + z)^2 + (y + z)^3 = x^3 + 3x^2y + 3x^2z + 3xy^2 + 6xyz + 3xz^2 + y^3 + 3y^2z + 3yz^2 + z^3 = x^3 + y^3 + z^3 + 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz.

Expand the following expression: (2a - 3b)(2a + 3b)

  1. 4a^2 - 9b^2

  2. 4a^2 + 9b^2

  3. 4a^2 - 12ab + 9b^2

  4. 4a^2 + 12ab + 9b^2

Show answer
Correct Option: A
Explanation:

To expand the expression, use the difference of squares formula: (2a - 3b)(2a + 3b) = (2a)^2 - (3b)^2 = 4a^2 - 9b^2.

Expand the following expression: (x^2 - 2x + 1)(x^2 + 2x + 1)

  1. x^4 - 1

  2. x^4 + 1

  3. x^4 - 4x^2 + 1

  4. x^4 + 4x^2 + 1

Show answer
Correct Option: B
Explanation:

To expand the expression, use the sum of squares formula: (x^2 - 2x + 1)(x^2 + 2x + 1) = (x^2)^2 - (2x)^2 = x^4 - 4x^2 + 1.

Expand the following expression: (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)

  1. a^3 + b^3 + c^3 - 3abc

  2. a^3 + b^3 + c^3 + 3abc

  3. a^3 + b^3 + c^3

  4. a^3 + b^3 + c^3 - ab - bc - ca

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property and combine like terms: (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) = a(a^2 + b^2 + c^2 - ab - bc - ca) + b(a^2 + b^2 + c^2 - ab - bc - ca) + c(a^2 + b^2 + c^2 - ab - bc - ca) = a^3 + a^2b + a^2c - a^2b - ab^2 - abc + b^3 + b^2a + b^2c - b^2a - bc^2 - abc + c^3 + c^2a + c^2b - c^2a - ca^2 - abc = a^3 + b^3 + c^3 - 3abc.

Expand the following expression: (x - y - z)^3

  1. x^3 - y^3 - z^3 - 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz

  2. x^3 - y^3 - z^3 + 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) - 6xyz

  3. x^3 - y^3 - z^3 + 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz

  4. x^3 - y^3 - z^3 - 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) - 6xyz

Show answer
Correct Option: A
Explanation:

To expand the expression, use the cube of a binomial formula: (x - y - z)^3 = x^3 - 3x^2(y + z) + 3x(y + z)^2 - (y + z)^3 = x^3 - 3x^2y - 3x^2z + 3xy^2 + 6xyz + 3xz^2 - y^3 - 3y^2z - 3yz^2 - z^3 = x^3 - y^3 - z^3 - 3(x^2y + xy^2 + xz^2 + yx^2 + yz^2 + zy^2) + 6xyz.

Expand the following expression: (2x + 3y)(3x - 2y)

  1. 6x^2 - 9xy - 6y^2

  2. 6x^2 + 9xy - 6y^2

  3. 6x^2 - 9xy + 6y^2

  4. 6x^2 + 9xy + 6y^2

Show answer
Correct Option: A
Explanation:

To expand the expression, use the distributive property: (2x + 3y)(3x - 2y) = 2x(3x - 2y) + 3y(3x - 2y) = 6x^2 - 4xy + 9xy - 6y^2 = 6x^2 - 9xy - 6y^2.

Expand the following expression: (x^2 + 2x + 1)(x - 1)

  1. x^3 - 1

  2. x^3 + 1

  3. x^3 - x^2 - 2x - 1

  4. x^3 + x^2 + 2x + 1

Show answer
Correct Option: C
Explanation:

To expand the expression, use the distributive property: (x^2 + 2x + 1)(x - 1) = x^2(x - 1) + 2x(x - 1) + 1(x - 1) = x^3 - x^2 + 2x^2 - 2x + x - 1 = x^3 + x^2 - 2x - 1.

Expand the following expression: (a^3 - b^3)(a + b)

  1. a^4 - b^4

  2. a^4 + b^4

  3. a^4 - a^3b - ab^3 + b^4

  4. a^4 + a^3b + ab^3 + b^4

Show answer
Correct Option: C
Explanation:

To expand the expression, use the distributive property: (a^3 - b^3)(a + b) = a^3(a + b) - b^3(a + b) = a^4 + a^3b - a^3b - b^4 = a^4 - a^3b - ab^3 + b^4.

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