Question

What is the factorization of 36b^4 – 64?

Answer 1

4(3b² + 4)(3b² - 4)

Explanation:

Given

36
`b^(4)` - 64 ← factor out 4 from each term

= 4(9
`b^(4)` - 16) ← factor as a difference of squares

a² - b² = (a + b)(a - b), thus

9
`b^(4)` - 16

= (3b²)² - 4²

= (3b² + 4)(3b² - 4)

Hence

36
`b^(4)` - 64

= 4(3b² + 4)(3b² - 4) ← in factored form