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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

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

A
-55x² + 25y²
B
-54x² - 25y²
C
54x² + 25y²
D
55x² - 25y²
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
Simplify: (5x - 2y)² + (2x + 5y)² + (5x + 2y)(5x - 2y)
Correct Answer
54x² + 25y²
Algebraic Expansion: First, expand the squared binomials using standard identities: (5x - 2y)² results in 25x² - 20xy + 4y², and (2x + 5y)² results in 4x² ......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Algebraic Expansion ▼
First, expand the squared binomials using standard identities: (5x - 2y)² results in 25x² - 20xy + 4y², and (2x + 5y)² results in 4x² + 20xy + 25y².
Difference of Squares ▼
Next, expand the third component using the (a + b)(a - b) = a² - b² identity. Thus, (5x + 2y)(5x - 2y) transforms into 25x² - 4y².
Combining Like Terms ▼
Add all expanded sections together: (25x² - 20xy + 4y²) + (4x² + 20xy + 25y²) + (25x² - 4y²). The middle terms (-20xy and +20xy) cancel out perfectly. Similarly, +4y² and -4y² nullify each other.
Final Addition ▼
The remaining terms are 25x² + 4x² + 25y² + 25x², which equals 54x² + 25y².
Conclusion ▼
The accurately simplified expression is 54x² + 25y².
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