Algebra 2 quadratic trinomials help please

I already have the answers so I just need help showing the work.

Question: Use the formula for factoring quadratic trinomials to factor each expressions below?

A. x^4-10x^2+21
Answer: (x^2-3)(x^2-7)

B. 49x^4-16
Answer: (7x^2+4)(7x^2-4)

C. x^4+19x^2+60
Answer: (x^2+15)(x^2+4)

A- x^4 - 10x^2 + 21=0
Let us suppose x^2 = a
Than equation === a^2-10a+21=0
a^2-7a-3a+21=0
a(a-7)-3(a-7)=0
(a-7)(a-3)
let put a=x^2
(x^2-7)(x^2-3) answer

B--
49x^4- 16
use formula= (a^2-b^2)=(a+b)(a-b)
49x^49-16= (7x^2-4)(7x^2+4) Answer

C----
x^4+19x^2+60
let us suppose x^2 = a
a^2+19a+60
a^2+15a+4a+60
a(a+15)+4(a+15)
(a+15)(a+4)
put a=x^2
than
( x^2+15)(x^2+4) Answer

Let u=x^2. These are quadratics in disguise.

A is then transformed to: u^2-10u+21=(u-3)(u-7)=(x^2-3)(x^2-7)
Exactly the same technique for the other 2.

There is no such formula. You factor in your head. It is a pain in the _____!