Factor completely, if possible..please?

Question

1/25+1/10t^2+1/16t^4

the variable "t" isn't exclusive to the denominator, it's part of both fractions...

I think it's (1/4t^2+1/5)(1/4t^2+1/5) but what do I know? lol

Please help.. thanks in advance.

Answer 1

as you correctly pointed out, your trinomial is a square indeed:

1/25 + (1/10) t^2 + (1/16) t^4 =

[1/5 + (1/4) t^2]^2

in fact expanding it back, you get:

(1/25) + (1/16) t^4 + 2(1/5)(1/4) t^2 = (1/25) + (1/16) t^4 + 2(1/20) t^2 =

(1/25) + (1/16) t^4 + (1/10) t^2

[1/5 + (1/4) t^2] is no further factorable, so your answer is correct

I hope it helps..

Bye!