Factorize and simplify

Question

64x⁶-15625y¹²

Answer 1

To factorize and simplify 64x⁶ - 15625y¹², we need to find the common factors between the terms.

Finding the common factors:
64x⁶ = (4x³)²
15625y¹² = (125y⁴)²

Now, we can rewrite the expression as:
(4x³)² - (125y⁴)²

This is a difference of squares, so we can use the formula (a² - b²) = (a + b)(a - b) to simplify the expression:

((4x³) + (125y⁴))((4x³) - (125y⁴))

Therefore, the factored and simplified form of 64x⁶ - 15625y¹² is:
(4x³ + 125y⁴)(4x³ - 125y⁴)