Question

(x+y+z) ka whole cube - (y+z-x) ka whole cube

Answer 1

(x+y+z)^3 - (y+z-x)^3 - (z+x-y)^3 - (x+y-z)^3 --------- rearrange the terms 
= [(x+y+z)^3 - (y+z-x)^3] + [(y-z-x)^3 - (x+y-z)^3 
Let (y + z) = a and (y – z) = b 

= [(a+x)³ – (a-x)³] + [(b-x)³ – (b+x)³] 
= [(a³+x³ + 3ax(a+x) – {a³-x³-3ax(a-x)]] + [(b³-x³– 3bx(b-x) – {(b³+x³+3bx(b+x)] 
= [(a³+x³ + 3ax(a+x) – a³+x³+3ax(a-x)] + [(b³-x³– 3bx(b-x) – b³-x³-3bx(b+x)] 
= [(2x³ + 3ax(a+x+a-x)] + [(-2x³– 3bx(b-x+b+x)] 
= 3ax(a+a)] – 3bx(b+b) 
= 6a²x – 6b²x 
= 6x(a² – b²) 
= 6x(a – b)(a + b) 
= 6x(y+z – y+z)(y+z +y – z) 
= 6x(z+z)(y+y) 
= 6x(2z)(2y) 
= 24xyz .


I hope this will help you