Question

The coefficient of the third term in the expansion of the binomial (3x^2+2y^3)^4 is?

Answer 1

(3x² + 2y³)⁴
(3x² + 2y³)²(3x² + 2y³)²
(3x² + 2y³)(3x² + 2y³)(3x² + 2y³)(3x² + 2y³)
(3x²(3x² + 2y³) + 2y³(3x² + 2y³))(3x²(3x² + 2y³) + 2y³(3x² + 2y³))
(3x²(3x²) + 3x²(2y³) + 2y³(3x²) + 2y³(2y³))(3x²(3x²) + 3x²(2y³) + 2y³(3x²) + 2y³(2y³))
(6x⁴ + 6x²y³ + 6x²y³ + 4y⁶)(6x⁴ + 6x²y³ + 6x²y³ + 4y⁶)
(6x⁴ + 12x²y³ + 4y⁶)(6x⁴ + 12x²y³ + 4y⁶)
6x⁴(6x⁴ + 12x²y³ + 4y⁶) + 12x²y³(6x⁴ + 12x²y³ + 4y⁶) + 4y⁶(6x⁴ + 12x²y³ + 4y⁶)
6x⁴(6x⁴) + 6x⁴(12x²y³) + 6x⁴(4y⁶) + 12x²y³(6x⁴) + 12x²y³(12x²y³) + 12x²y³(4y⁶) + 4y⁵(6x⁴) + 4y⁶(12x²y³) + 4y⁶(4y⁶)
24x⁸ + 72x⁶y³ + 24x⁴y⁶ + 72x⁶y³ + 144x⁴y⁶ + 48x²y⁹ + 24x⁴y⁵ + 48x²y⁹ + 16y¹²
24x⁸ + 72x⁶y³ + 72x⁶y³ + 24x⁴y⁶ + 144x⁴y⁶ + 48x²y⁹ + 48x²y⁹ + 24x⁴y⁵ + 16y¹²
24x⁸ + 144x⁶y³ + 168x⁴y⁶ + 96x²y⁹ + 24x⁴y⁵ + 16y¹²

The coefficient of the third term in the expansion of the binomial is 6.