Pariksha SaathiQuantitative Aptitude
Algebraic Identities: Practice Questions with Answers
14 practice questions on Algebraic Identities, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
If a−b = 4 and ab = 12, find a² + b².
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Answer: 40
Solution:
- a² + b² = (a−b)² + 2ab.
- = 4² + 2(12) = 16 + 24 = 40.
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Q.2
Simplify using identities: 97 × 103
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Answer: 9,991
Solution:
- 97 × 103 = (100−3)(100+3) = 100² − 3².
- = 10,000 − 9 = 9,991.
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Q.3
Factor completely: x³ − 8
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Answer: (x − 2)(x² + 2x + 4)
Solution:
- Write 8 as 2³, then apply the difference of cubes: x³ − 2³ = (x − 2)(x² + 2x + 4).
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Q.4
If a+b = 10 and ab = 21, find a² + b².
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Answer: 58
Solution:
- a² + b² = (a+b)² − 2ab.
- = 10² − 2(21) = 100 − 42 = 58.
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Q.5
If a−b = 3 and ab = 10, find a³ − b³.
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Answer: 117
Solution:
- a³−b³ = (a−b)³ + 3ab(a−b).
- = 3³ + 3(10)(3) = 27 + 90
- = 117.
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Q.6
If a+b = 5 and ab = 6, find a³ + b³.
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Answer: 35
Solution:
- a³+b³ = (a+b)³ − 3ab(a+b).
- = 5³ − 3(6)(5) = 125 − 90
- = 35.
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Q.7
If a+b = 7 and a² + b² = 25, find ab.
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Answer: 12
Solution:
- (a+b)² = a² + 2ab + b², so 49 = 25 + 2ab.
- 2ab = 24, so ab = 12.
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Q.8
If a+b = 6 and ab = 8, find a³ + b³.
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Q.9
Simplify using identities: 95 × 105
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Q.10
If a−b = 2 and ab = 15, find a³ − b³.
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Q.11
If a−b = 6 and a² + b² = 58, find ab.
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Q.12
If a+b = 12 and ab = 27, find a² + b².
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Q.13
Factor completely: x³ − 27
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Q.14
Simplify using identities: 998 × 1002
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.