Trigonometric Identities (Simplification)

Question

Question-

(Please show all of your work when answering the question. It helps me out quite a bit. Thank you in advance. -Student)

(2sinx+2cosx)^2 + (2sinx-2cosx)^2

Answer 1

(2sinx+2cosx)^2 + (2sinx-2cosx)^2

= 4sin^2(x) +8sinxcosx + 4cos^2(x)

+ 4sin^2(x) - 8sinxcosx + 4cos^2(x)

= 8(sin^2(x) + cos^2(x))

= 8(1)

= 8