MCQ practice · SSC General Mathematics Board questions · Chapter 3: Algebraic Expressions
(x + 3y − z)² = ?
Think it through first, then pick an option.
- a x² + 9y² + z² + 3xy − 6yz − 2zx
- b x² + 9y² + z² + 6xy − 6yz − 2zx
- c x² + 9y² + z² − 6xy − 6yz + 2zx
- d x² + 9y² + z² + 6xy − 3yz − 2zx
Answer and explanation
Correct answer: b x² + 9y² + z² + 6xy − 6yz − 2zx
Squares x², 9y², z²; cross terms +6xy (both +), −6yz (3y and −z), −2zx (x and −z).
Why the other options are wrong
- a x² + 9y² + z² + 3xy − 6yz − 2zx: The xy term should be 2 × x × 3y = 6xy; here 3xy is used and the factor 2 is lost.
- c x² + 9y² + z² − 6xy − 6yz + 2zx: The xy term would be −6xy only if one of x and 3y were negative; both are positive. And the zx term is −, not +.
- d x² + 9y² + z² + 6xy − 3yz − 2zx: The yz term is 2 × 3y × (−z) = −6yz; here −3yz is used and the factor 2 is lost.
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