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NTPC Graduate Tier 1 2025 Shift-1 📅 06 May, 2025

Simplify (2x - 5y)² + (5x + 2y)² + (2x + 5y)(2x - 5y).

A
34x² - 4y²
B
-34x² + 4y²
C
-33x² - 4y²
D
33x² + 4y²
Result Summary
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NTPC Graduate Tier 1
2025 • 06 May, 2025 • Shift-1
Simplify (2x - 5y)² + (5x + 2y)² + (2x + 5y)(2x - 5y).
Correct Answer
33x² + 4y²
Systematic Expansion of Squares: We must rigorously apply the standard algebraic identity (a ± b)². Consequently, the first term expands gracefully ......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Systematic Expansion of Squares ▼
We must rigorously apply the standard algebraic identity (a ± b)². Consequently, the first term expands gracefully into 4x² - 20xy + 25y². Following the same logic, the second term expands into 25x² + 20xy + 4y².
Evaluating the Difference of Squares ▼
The third and final component strictly adheres to the well-known (a+b)(a-b) difference of squares identity, which translates directly into the expansion 4x² - 25y².
Phase One Combining of Terms ▼
Summing the initial two expansions together yields an intermediate subtotal of 29x² + 29y² (this occurs seamlessly because the troublesome -20xy and +20xy cross-terms perfectly cancel each other out).
Final Stage Simplification ▼
Fusing the third expansion (4x² - 25y²) to this established sum results in combining like terms: (29x² + 4x²) alongside (29y² - 25y²).
Conclusion ▼
The final, fully consolidated and mathematically sound algebraic expression is strictly 33x² + 4y².
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