Question

How do you factor `15r^2-16rt+4t^2`?

Answer 1

`15r^2-16rt+4t^2=(5r - 2t)(3r - 2t)`

Explanation:

We need to know the factors of 15 and 4 that will provide a sum of 16

factors of 15=3 and 5
factors of 4 = 2 an 2

By inspection , we have the numbers 2, 2, 3 , 5
We can now use the combination of 2(3) + 2(5)=6+10=16 which is the number at the middle term.

To use these numbers in factoring the arrangement should be

`(5r - 2t)(3r - 2t)=5r(3r)-2t(3r)-5r(2t)+2t(2t)`
`=15r^2-16rt+4t^2`

God bless....I hope the explanation is useful.