Quantitative Aptitude ยท Mathematics

Algebraic Simplification

146 Questions

Algebraic simplification involves reducing mathematical expressions to their simplest forms using exponent rules and identities. Test takers must manipulate equations to find rapid solutions. This skill is frequently assessed in SSC, banking, and railway quantitative aptitude sections.

Exponent rulesSurd operationsAlgebraic identitiesTrigonometric simplificationLogical expressions

Algebraic Simplification Questions

Multiple choice

Simplify the expression: (\sqrt{16} + \sqrt{25})

  1. \(5\)
  2. \(7\)
  3. \(10\)
  4. \(12\)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simplify each square root: (\sqrt{16} = 4) and (\sqrt{25} = 5). Add the simplified values: (4 + 5 = 10).

Multiple choice

Simplify the expression: (\frac{1}{2}x - \frac{1}{3}y + \frac{1}{4}x - \frac{1}{6}y)

  1. \(\frac{3}{4}x - \frac{1}{2}y\)
  2. \(\frac{5}{6}x - \frac{1}{2}y\)
  3. \(\frac{3}{4}x - \frac{5}{6}y\)
  4. \(\frac{5}{6}x - \frac{3}{4}y\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Combine like terms: (\frac{1}{2}x + \frac{1}{4}x - \frac{1}{3}y - \frac{1}{6}y = \frac{3}{4}x - \frac{1}{2}y).

Multiple choice

Simplify the expression: (\frac{2}{3}x + \frac{1}{2}y - \frac{1}{6}x + \frac{3}{4}y)

  1. \(\frac{1}{2}x + \frac{5}{4}y\)
  2. \(\frac{1}{2}x + \frac{7}{6}y\)
  3. \(\frac{5}{6}x + \frac{5}{4}y\)
  4. \(\frac{5}{6}x + \frac{7}{6}y\)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combine like terms: (\frac{2}{3}x - \frac{1}{6}x + \frac{1}{2}y + \frac{3}{4}y = \frac{5}{6}x + \frac{7}{6}y).

Multiple choice

Simplify the expression (log_a (a^3 b^2)).

  1. \(3 log_a a + 2 log_a b\)
  2. \(3 + 2 log_a b\)
  3. \(log_a a^3 + log_a b^2\)
  4. \(3 log_a a b^2\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the logarithmic property (log_b (b^n) = n), we have (log_a (a^3 b^2) = log_a a^3 + log_a b^2 = 3 log_a a + 2 log_a b = 3 + 2 log_a b).

Multiple choice

Simplify the expression (log_a (a^2 b^3 c^4)).

  1. \(2 log_a a + 3 log_a b + 4 log_a c\)
  2. \(2 + 3 log_a b + 4 log_a c\)
  3. \(log_a a^2 + log_a b^3 + log_a c^4\)
  4. \(2 log_a a b^3 c^4\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the logarithmic property (log_b (b^n) = n), we have (log_a (a^2 b^3 c^4) = log_a a^2 + log_a b^3 + log_a c^4 = 2 log_a a + 3 log_a b + 4 log_a c = 2 + 3 log_a b + 4 log_a c).

Multiple choice

Simplify the expression (log_a (a^5 b^2 c^3)).

  1. \(5 log_a a + 2 log_a b + 3 log_a c\)
  2. \(5 + 2 log_a b + 3 log_a c\)
  3. \(log_a a^5 + log_a b^2 + log_a c^3\)
  4. \(5 log_a a b^2 c^3\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the logarithmic property (log_b (b^n) = n), we have (log_a (a^5 b^2 c^3) = log_a a^5 + log_a b^2 + log_a c^3 = 5 log_a a + 2 log_a b + 3 log_a c = 5 + 2 log_a b + 3 log_a c).

Multiple choice

Simplify the expression (log_a (a^7 b^4 c^5)).

  1. \(7 log_a a + 4 log_a b + 5 log_a c\)
  2. \(7 + 4 log_a b + 5 log_a c\)
  3. \(log_a a^7 + log_a b^4 + log_a c^5\)
  4. \(7 log_a a b^4 c^5\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the logarithmic property (log_b (b^n) = n), we have (log_a (a^7 b^4 c^5) = log_a a^7 + log_a b^4 + log_a c^5 = 7 log_a a + 4 log_a b + 5 log_a c = 7 + 4 log_a b + 5 log_a c).

Multiple choice

Simplify the expression: 8 - (3 + 2).

  1. 1

  2. 3

  3. 5

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To simplify the expression, follow the order of operations (parentheses first): 8 - (3 + 2) = 8 - 5 = 3. Therefore, the answer is 3.

Multiple choice

Simplify the expression: (x^2 + 2x + 1) - (x^2 - 3x + 2).

  1. 5x - 1

  2. 5x + 1

  3. 5x - 3

  4. 5x + 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify the expression, combine like terms: (x^2 + 2x + 1) - (x^2 - 3x + 2) = x^2 + 2x + 1 - x^2 + 3x - 2 = 5x - 1. Therefore, the answer is 5x - 1.

Multiple choice

Simplify the expression: (3x + 2y) + (4x - 3y)

  1. 7x - y

  2. 7x + y

  3. 7x - 5y

  4. 7x + 5y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Combine like terms: (3x + 4x) + (2y - 3y) = 7x - y.

Multiple choice

Simplify the expression: (2a^2 + 3ab) - (a^2 - 2ab)

  1. a^2 + 5ab

  2. a^2 - 5ab

  3. 3a^2 + 5ab

  4. 3a^2 - 5ab
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combine like terms: (2a^2 - a^2) + (3ab + 2ab) = a^2 + 5ab.

Multiple choice

Simplify the expression: (x + 3)(x - 2)

  1. x^2 + x - 6

  2. x^2 - x - 6

  3. x^2 + 5x - 6

  4. x^2 - 5x - 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the distributive property: (x + 3)(x - 2) = x^2 - 2x + 3x - 6 = x^2 + x - 6.

Multiple choice

Simplify the expression: (2x^2y^3)(3xy^2)

  1. 6x^3y^5

  2. 6x^3y^6

  3. 6x^2y^5

  4. 6x^2y^6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Multiply the coefficients and combine like terms: (2x^2y^3)(3xy^2) = 6x^3y^5.

Multiple choice

Simplify the expression: (a + b)^2

  1. a^2 + 2ab + b^2

  2. a^2 - 2ab + b^2

  3. a^2 + b^2

  4. a^2 - b^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.

Multiple choice

Simplify the expression: (x - 3)^3

  1. x^3 - 9x^2 + 27x - 27

  2. x^3 + 9x^2 + 27x + 27

  3. x^3 - 9x^2 - 27x - 27

  4. x^3 + 9x^2 - 27x + 27
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the formula for cubing a binomial: (x - 3)^3 = x^3 - 3x^2(3) + 3x(3^2) - 3^3 = x^3 - 9x^2 + 27x - 27.