Answer:
Option 4 is the correct answer 48x⁹ - 72x⁷ + 36x⁵
Step-by-step explanation:
The given expression is,
9x⁵ + 3x(4x⁴ - 3x²)²
To find (4x⁴ - 3x²)²
(a + b)² = a² + 2ab + b²
(4x⁴ - 3x²)² = (4x⁴ )² - 2*4x⁴*3x² + (3x²)²
= 16x⁸ - 24x⁴⁶+ 9x⁴
To find 3x(4x⁴ - 3x²)²
(4x⁴ - 3x²)² =16x⁸ - 24x⁶+ 9x⁴
3x(4x⁴ - 3x²)² = 3x(16x⁸ - 24x⁶+ 9x⁴ ) = 48x⁹ - 72x⁷ +27x⁵
To find 9x⁵ + 3x(4x⁴ - 3x²)²
3x(4x⁴ - 3x²)² = 48x⁹ - 72x⁷ +27x⁵
9x⁵ + 3x(4x⁴ - 3x²)² = 9x⁵+ 48x⁹ - 72x⁷ +27x⁵ = 48x⁹ - 72x⁷ +36x⁵
Therefore the option 4 is the correct answer
