Question

Factorise the following:

625a⁴ – 256b⁴

Answer 1

To factorize 625a⁴ – 256b⁴, we can use the difference of squares formula, which is given by:

A² – B² = (A – B)(A + B)

Here, we have:

625a⁴ – 256b⁴

This can be written as

(25a²)² – (16b²)²

Now, applying the difference of squares formula

(25a² – 16b²)(25a² + 16b²)

Next, notice that 25a² – 16b² is also a difference of squares

25a² – 16b² = (5a – 4b)(5a + 4b)

Thus, the complete factorisation of 625a⁴ – 256b⁴ is (5a – 4b)(5a + 4b)(25a² + 16b²)