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 general knowledge math & puzzles

(A+B)^2

  1. A^2 + B^2 + 2xAxB

  2. A^2 + B^2 - 2xAxB

  3. A^2 + B^2

  4. NO IDEA
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square of a binomial (A+B)^2 is calculated as (A+B)(A+B) = A^2 + AB + BA + B^2, which simplifies to A^2 + B^2 + 2AB. Option 407806 is the standard mathematical identity.

Multiple choice general knowledge math & puzzles

(A-B)^2

  1. A^2 + B^2 + 2xAxB

  2. A^2 + B^2 - 2xAxB

  3. A^2 - B^2

  4. (A-B)X(A+B)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The algebraic identity (A - B)² expands to A² - 2AB + B², which can be written as A² + B² - 2AB. This is derived by multiplying (A - B)(A - B) using the distributive property. Option A incorrectly shows +2AB instead of -2AB.

Multiple choice general knowledge math & puzzles

(A+B)^3

  1. A^3+B^3+2AB(A+B)

  2. A^3+B^3+3AB(A+B)

  3. A^3+B^3+2AB(A^2+B^2)

  4. A^3+B^3+AB(A^2+B^2)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The expansion of (A + B)³ is A³ + 3A²B + 3AB² + B³, which can be factored as A³ + B³ + 3AB(A + B). This is a standard algebraic identity. Option A incorrectly uses 2AB instead of 3AB, while options C and D have incorrect structures.

Multiple choice general knowledge math & puzzles

(A-B)^3

  1. A^3-B^3-3xAxB(A-B)

  2. A^3+B^3+3xAxB(A-B)

  3. A^3+B^3-3xAxB(A+B)

  4. A^3+B^3+3xAxB(A+B)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The algebraic expansion of (A-B)^3 is A^3 - B^3 - 3AB(A-B). This can also be written as A^3 - 3A^2B + 3AB^2 - B^3. Option 407822 correctly represents the factored form of the subtraction terms.

Multiple choice general knowledge

5^0 + 1^15 - 8^0 - 1^23

  1. 3

  2. 4

  3. 0

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Remember that any non-zero number raised to the power 0 equals 1: 5^0 = 1, 1^15 = 1, 8^0 = 1, 1^23 = 1. So 1 + 1 - 1 - 1 = 0. Option C is correct. A common mistake is forgetting that 1 raised to any power is still 1.

Multiple choice general knowledge

2^2 + 5^2 + 2x2x5

  1. 59

  2. 35

  3. 49

  4. 69
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate each term: 2^2 = 4, 5^2 = 25, 2 x 2 x 5 = 20. Sum: 4 + 25 + 20 = 49. This is the expansion of (a + b)^2 = a^2 + b^2 + 2ab where a = 2 and b = 5, so (2 + 5)^2 = 49. Option C is correct.

Multiple choice general knowledge

5^3 x 3^4 x 0^6 x 1^5

  1. 1

  2. 16

  3. 15

  4. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

One factor is 0^6. Any non-zero number raised to any positive power is still non-zero, but when multiplied by 0, the entire product becomes 0. Option D is correct. The other terms (5^3 = 125, 3^4 = 81, 1^5 = 1) don't matter once 0 appears.

Multiple choice general knowledge math & puzzles

1^2+2^2+3^2=?

  1. n(n+1)/2

  2. n(n+1)(2n+1)/6

  3. [n(n+1)]^2

  4. all of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formula for the sum of the squares of the first n natural numbers (1^2 + 2^2 + ... + n^2) is given by n(n+1)(2n+1)/6. The other options represent the sum of n numbers or the sum of cubes.

Multiple choice technology

FIELD ("+1+2+3ABAC","+", 2,2) =?

  1. 1

  2. 1+2

  3. 3ABAC

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The FIELD function extracts a substring between two occurrences of a delimiter. FIELD("+1+2+3ABAC", "+", 2, 4) means: find the substring between the 2nd and 4th occurrences of "+". The delimiters are at positions: 1st at 0, 2nd at 2, 3rd at 4, 4th at 6. The substring between positions 2 and 4 is "1+2".

Multiple choice

Find the sum of additive inverse and multiplicative inverse of the following expression? (abc/de)

  1. {(de)2 + (abc)2}/ abcde

  2. {(de)2 - (abc)2}/ abcde

  3. {(de)2 - (abc)2}/ abde

  4. {(de)2 - (abc)2}/ de

  5. {(de)2 - (abc)2}/ abc
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given expression is (abc/de). Additive inverse of the given expression is (- abc/de). Thus, abc/de - abc/de = 0 Multiplicative inverse of the given expression is (de/abc). Thus, abc/de x de/abc = 1 So, the required sum of additive inverse and multiplicative inverse = - abc/de + de/abc = {(de)2 - (abc)2}/ abcde