Question

I need to know how to factor 16a4-b4

Answer 1

16a⁴ - b⁴

Factorizing powers.

(4a²)² - (b²)²

(4a² + b²)(4a² - b²) by difference of two squares.

But (4a² - b²) is also difference of two squares.

(4a² - b²) = (2a)² - b² = (2a - b)(2a + b)

Therefore:

16a⁴ - b⁴ = (4a² + b²)(4a² - b²) = (4a² + b²)(2a - b)(2a + b)

16a⁴ - b⁴ = (4a² + b²)(2a - b)(2a + b)

Answer 2

This is a difference of two squares:

(16a^4 - b^4)

= (4a^2 + b^2) (4a^2 - b^2)

This can be further simplified as the second bracket is also a difference of two squares:

(4a^2 + b^2) (4a^2 - b^2)

= 4a^2 + b^2) (2a - b) (2a + b)