Factor completely. x^4 − 729x

Question

please help thanks

Answer 1

x⁴ − 729x

x(x³-729)

x(x³-9³)

 

Use the difference of cubes formula, (a³ − b³) = (a−b)(a²+ab+b²):

 

x(x³ - 9³) = x·(x - 9)(x² + 9x + 81)

 

The quadratic term does not factor.

 

Answer 2

Recall:  A³ - B³ = (A - B)(A² + AB + B²)

 

x⁴ - 729x = x(x³ - 9³)

 

              = x(x - 9)(x² + 9x + 81)