Question

Which expression is equivalent to

Answer 1

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