If z = (x + y)(^4) – (x – y)(^4), which of the following is equal to one half of one quarter of z?

A. x(^3)y(^3)
B. 8x(^3)y(^3)
C. x(^3)y + xy(^3)
D. 8x(^3)y + 8xy(^3)
E. x(^3)y – xy(^3)







z = (x + y)(^4) – (x – y)(^4),

They are asking for 1/2 . 1/4 . Z = 1/8 Z

= 1/8 [(x + y)(^4) – (x – y)(^4) ]

as you said we can apply the a2 - b2 formula

= 1/8 [ (x+y)2 +(x-y)2] [(x+y)2 -(x-y)2]

= 1/8 . [ x2 +y2 +2xy +x2 +y2 - 2xy] [x2 +y2 +2xy -x2 -y2 + 2xy]

= 1/8. [2x2+2y2] 2x.2y

= xy(x2+y2)

= x3y + xy3

= C