Mathematics · Quantitative Aptitude

Algebraic Expressions and Polynomials

275 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

What is (7x + 5) (4y + 5) in expanded form?

  1. 28xy + 26 + 37x + 21y

  2. 28xy + 26 + 37y + 21x

  3. 28xy + 25 + 35y + 20x

  4. 28xy + 25 + 35x + 20y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(7x + 5) (4y + 5) = 28xy + 35x + 20y + 25            (Using Foil)

Multiple choice

What is (m - n) (z + c) in expanded form?

  1. mz - nz + mc - nc

  2. mz + nz - mc - nc

  3. mz - nz - mc + nz

  4. mz - nz -<span style="font-family:" arial;="" font-size:="" small;=""> mc - nc
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(m - n) (z + c) = mz + mc - nz - nc (Using Foil)

Multiple choice

What is (6u + 5) (5v + 6u) in expanded form?

  1. 36u2 + 30u + 25v + 30uv

  2. 36u2 + 31u + 26v + 32uv

  3. 36u2 + 30u + 26v + 32uv

  4. 36u2 + 32u + 25v + 35uv
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(6u + 5) (5v + 6u) = 30uv + 36u2 + 25v + 30u                     (Using Foil) = 36u2 + 30u + 25v + 30uv

Multiple choice

What is (x - 6) (4y - 1) in expanded form?

  1. 4xy + 6 + x - 24y

  2. 4xy - 6 - x + 24y

  3. 4xy + 6 - x - 24y

  4. 4xy -<span style="font-family:" arial;="" font-size:="" small;=""> 6 + x - 24y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(x - 6) (4y - 1) = 4xy - x - 24y + 6 (Using Foil)

Multiple choice

What is (3x - 4) (4x + 3) in expanded form?

  1. 12x2 + 7x - 12

  2. 12x2 - 7x + 12

  3. 12x2 + 7x + 12

  4. 12x2 -<span style="font-family:" arial;="" font-size:="" small;=""> 7x - 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(3x - 4) (4x + 3) = 12x2 + 9x - 16x - 12 (Using Foil) = 12x2 - 7x - 12

Multiple choice

What is (4a + 2) (6a2 - a + 2) in expanded form?

  1. 24a3 + 8a2 + 6a + 4

  2. 24a3 - 8a2 + 6a + 4

  3. 24a3 - 8a2 + 4a + 6

  4. 24a3 - 8a2 - 6a + 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(4a + 2) (6a2 - a + 2) = 24a3 - 4a2 + 8a + 12a2 - 2a + 4 (Expanding brackets) = 24a3 - 4a2 + 12a2 + 8a - 2a + 4 = 24a3 + 8a2 + 6a + 4