a) A = (a-b-c)² - (a-b+c)²
= a²+b²+c²-2ab-2bc-2ac - (a²+b²+c²-2ab-2bc+2ac)
= a²+b²+c²-2ab-2bc-2ac -a²-b²-c²+2ab+2bc-2ac
= -4ac
b) B = (a-x-y)³ - (a+x-y)³
= [(a-x-y)-(a+x-y)][(a-x-y)²+(a-x-y)(a+x-y)+(a+x-y)²]
= (a-x-y-a-x+y)(a²+x²+y²-2ax-2ay+2xy+a²+ax-ay-ax-x²+xy-ay-xy+y²+a²+x²+y²+2ax-2ay-2xy)
= -2x( 3a²-6ay+x²+3y²)
= -2x[3(a²-2ay+y²)+x²]
= -2x[3(a-y)²+x²]
c) C = (1+x+x²)(1-x)(1+x)(1-x+x²)
= (1+x+x²)(1-x+x²)(1-x)(1+x)
= [1 - (x+x²)²](1 - x²)
= (1-x²-2x³-$x^{4}$ )(1-x²)
