Question

What is the factored form of 125x6 – 8?

Answer 1

Explanation:

125 = 5 *5 * 5 = 5³

8 = 2 * 2 *2 = 2³

125x⁶ - 8 = 5³(x²)³ - 2³

= (5x²)³ - 2³ { a³ - b³ = (a -b)(a² + ab + b²)

= (5x² - 2) ([5x²]² + 5x²*2 + 2²)

= (5x² - 2)(25x⁴ + 10x² + 4)

Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴