Concept:Use the law of indices xnxm=xm−n and (xm)n=xmn to combine the exponents.Explanation:Simplify each bracket separately:First: [xa2+b2xab]a+b=x(ab−a2−b2)(a+b).Second: [xbcxb2+c2]b+c=x(b2+c2−bc)(b+c).Third: [xc2+a2xca]c+a=x(ca−c2−a2)(c+a).Multiply: exponents add, so total exponent E=(ab−a2−b2)(a+b)+(b2+c2−bc)(b+c)+(ca−c2−a2)(c+a).Expand each term:(ab−a2−b2)(a+b)=a2b+ab2−a3−a2b−ab2−b3=−a3−b3.(b2+c2−bc)(b+c)=b3+b2c+bc2+c3−b2c−bc2=b3+c3.(ca−c2−a2)(c+a)=c2a+ca2−c3−c2a−a2c−a3=−c3−a3.Sum: (−a3−b3)+(b3+c3)+(−c3−a3)=−2a3.Thus the product equals x−2a3.Answer:x−2a3, which corresponds to option A.