How do you factor the trinomial #t^2 + 6tf - 16f^2#?

1 Answer
Mar 18, 2016

#(t-2f)(t+8f)#

Explanation:

If #at^2+btf+cf^2# is the trinomial, we have to split #b# in two parts, which add up to #b# and whose product is #ac#.

Here, in #t^2+6tf-16f^2#, we will have to spit #6# in two parts, so that the product of the two is #-16#.

It is apparent that these are #+8# and #-2# and hence #t^2+6tf-16f^2# can be written as

#t^2+8tf-2tf-16f^2# or

= #t(t+8f)-2(t+8f)# or

= #(t-2f)(t+8f)#