(2X^2+63y^2)(2x^2-63y^2)

$$\\(2x^2+63y^2)(2x^2-63y^2)\\$$

This is a difference of 2 squares problem so the answer is just

 

$$\\(2x^2)^2-(63y^2)^2\\\\
=4x^4-3969y^4$$

.

(2X^2+63y^2)(2x^2-63y^2)

 

Assuming x = X:

set: a = 2X^2 and b =  63y^2

 

(a + b)(a - b) = a^2 - b^2=

(2X^2)^2 - (63y^2)^2 =

4X^4 - 3969y^4

 

Assuming x =/= X:

 

(2X^2+63y^2)(2x^2-63y^2) 

 

Set: a = 2X^2, b= 63y^2 and c = 2x^2

(a + b)(c - b) = ac - ab + bc - b^2 = a(c - b) + b(c - b) =

(2X^2)(2x^2 - 63y^2) + (63y^2)(2x^2 - 63y^2) =

4(X^2)(x^2) - 126(X^2)(y^2) + 126(x^2)(y^2) - 3969 y^4