How do you factor 20r^4-45n^420r445n4?

1 Answer
Feb 27, 2017

We can factor this using the following rule:

a^2 - b^2 = (a - b)(a + b)a2b2=(ab)(a+b)

Let a^2 = 20r^4a2=20r4 therefore sqrt(a^2) = a = sqrt(20r^4) = sqrt(20)r^2a2=a=20r4=20r2

Let b^2 = 45n^4b2=45n4 therefore sqrt(b^2) = b = sqrt(45n^4) = sqrt(45)n^2b2=b=45n4=45n2

Substituting gives:

20r^4 - 45n^4 = (sqrt(20)r^2 - sqrt(45)n^2)(sqrt(20)r^2 + sqrt(45)n^2)20r445n4=(20r245n2)(20r2+45n2)