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

1 Answer

Answer:

#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.