Question

How do you factor `20r^4-45n^4`?

Answer 1

We can factor this using the following rule:

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

Let `a^2 = 20r^4` therefore `sqrt(a^2) = a = sqrt(20r^4) = sqrt(20)r^2`

Let `b^2 = 45n^4` therefore `sqrt(b^2) = b = sqrt(45n^4) = sqrt(45)n^2`

Substituting gives:

`20r^4 - 45n^4 = (sqrt(20)r^2 - sqrt(45)n^2)(sqrt(20)r^2 + sqrt(45)n^2)`