Start learning →

DSSSB TGT Algebraic Identities — practice questions

Explore 12 free Algebraic Identities questions in DSSSB TGT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Algebraic Identities with Quill →

Algebraic Identities questions and exercises with answers

Showing questions 1–12 of 12.

The algebraic identity (a + b)² is equal to:Read the answer and worked solution →The identity (a − b)² is equal to:Read the answer and worked solution →The identity (a + b)(a − b) equals:Read the answer and worked solution →Use an identity to compute 102² quickly:Read the answer and worked solution →Compute 98² using an identity:Read the answer and worked solution →Compute 47 × 53 using an identity:Read the answer and worked solution →Factorise: 9x² − 25y²:Read the answer and worked solution →Find the value of x² + y² if x + y = 10 and xy = 21:Read the answer and worked solution →If a + b = 7 and a − b = 3, find a² − b²:Read the answer and worked solution →Find (x − 1/x)² if x + 1/x = 4:Read the answer and worked solution →Is (a + b)² > a² + b² always true for non-zero a, b?Read the answer and worked solution →Expand (2x + 3y)²:Read the answer and worked solution →

Worked practice questions

The algebraic identity (a + b)² is equal to:

  1. a² + b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab + b²
Show answer and solution

Correct answer: C. a² + 2ab + b²

**By expanding:** (a + b)² = (a + b)(a + b) = a² + ab + ba + b² = a² + 2ab + b². This holds for all real values of a and b.

Open this question →

The identity (a − b)² is equal to:

  1. a² − b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab − b²
Show answer and solution

Correct answer: B. a² − 2ab + b²

We have (a − b)² = (a − b)(a − b). That is (a − b)² = a² − ab − ba + b². So (a − b)² = a² − 2ab + b². The middle term is negative, distinguishing this from (a + b)².

Open this question →

The identity (a + b)(a − b) equals:

  1. a² + b²
  2. a² − b²
  3. a² + 2ab + b²
  4. 2ab
Show answer and solution

Correct answer: B. a² − b²

(a + b)(a − b) = a² − ab + ba − b² = a² − b². The cross terms cancel. This 'difference of squares' identity is one of the most useful in factorisation.

Open this question →

How to practise

  1. Choose a Algebraic Identities question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

SequencesBinomial TheoremGeometryProbability & StatisticsSequences and SeriesVectors & 3D GeometryProbabilityCorrelation and Regression