Mathematics ยท Quantitative Aptitude

Algebraic Expressions and Polynomials

292 Questions

Algebraic expressions and polynomials form the foundation of algebra, involving variables, constants, and mathematical operations. This topic is heavily tested in the quantitative aptitude sections of SSC, banking, and state exams. Use these questions to practice expanding, factoring, and simplifying various polynomial expressions.

Expanding algebraic expressionsFactoring polynomialsAlgebraic identitiesFinding common factorsSimplifying numerical statements

Algebraic Expressions and Polynomials Questions

Multiple choice

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

  1. x + 5y

  2. x + y

  3. 2x + y

  4. 3x + y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify the expression, combine like terms: (2x + 3y) - (x - 2y) = 2x + 3y - x + 2y = x + 5y. Therefore, the answer is x + 5y.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.