What is the value of (31^2 + 32^2)?
Answer and explanation
Correct answer: 1985
By direct calculation: 31^2 = 961 and 32^2 = 1024, so 961 + 1024 = 1985.
Alternatively use the identity
((n-1)^2 + n^2 = 2n^2 - 2n + 1) with n = 32:
2·32^2 - 2·32 + 1 = 2·1024 - 64 + 1 = 1985.
Common distractor (1975) results from arithmetic slip when squaring or adding. Exam tip: use algebraic identities or split squares (e.g. 32^2 = (30+2)^2) for faster, less error-prone calculation.
Frequently asked questions
What is the correct answer to this question?
1985
Why is this the correct answer?
By direct calculation: 31^2 = 961 and 32^2 = 1024, so 961 + 1024 = 1985.
Alternatively use the identity
((n-1)^2 + n^2 = 2n^2 - 2n + 1) with n = 32:
2·32^2 - 2·32 + 1 = 2·1024 - 64 + 1 = 1985.
Common distractor (1975) results from arithmetic slip when squaring or adding. Exam tip: use algebraic identities or split squares (e.g. 32^2 = (30+2)^2) for faster, less error-prone calculation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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