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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

Simplify the following.

(2x + 3)² - (x + 1)²

A
3x² + 10x + 8
B
4x² + 12x + 8
C
4x² + 10x + 6
D
3x² + 7x + 6
Result Summary
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APEDIA

NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
Simplify the following.

(2x + 3)² - (x + 1)²
Correct Answer
3x² + 10x + 8
Identity Application: To break down the expression, apply the standard algebraic identity (a + b)² = a² + 2ab + b² to both isolated terms.Expansion Phase: Th......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Identity Application ▼
To break down the expression, apply the standard algebraic identity (a + b)² = a² + 2ab + b² to both isolated terms.
Expansion Phase ▼
The first bracket transforms to (2x)² + 2(2x)(3) + (3)² = 4x² + 12x + 9. The second bracket transforms to (x)² + 2(x)(1) + (1)² = x² + 2x + 1.
Subtraction Phase ▼
Now mathematically combine them: (4x² + 12x + 9) - (x² + 2x + 1).
Distribution & Grouping ▼
Distribute the negative sign resulting in 4x² + 12x + 9 - x² - 2x - 1. Group the like variables together: (4x² - x²) + (12x - 2x) + (9 - 1).
Conclusion ▼
The final collapsed equation equals 3x² + 10x + 8.
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