Simplify the expression below?

(a^3 (b+c))/((a-b)(a-c)) + (b^3 (c+a))/((b-c)(b-a)) + (c^3 (a+b))/((c-a)(c-b))a3(b+c)(ab)(ac)+b3(c+a)(bc)(ba)+c3(a+b)(ca)(cb)

1 Answer
Jul 27, 2017

(a^3 (b+c))/((a-b)(a-c)) + (b^3 (c+a))/((b-c)(b-a)) + (c^3 (a+b))/((c-a)(c-b))a3(b+c)(ab)(ac)+b3(c+a)(bc)(ba)+c3(a+b)(ca)(cb)

=ab+bc+ca=ab+bc+ca

Explanation:

(a^3 (b+c))/((a-b)(a-c)) + (b^3 (c+a))/((b-c)(b-a)) + (c^3 (a+b))/((c-a)(c-b))a3(b+c)(ab)(ac)+b3(c+a)(bc)(ba)+c3(a+b)(ca)(cb)

hArr-(a^3(b+c))/((a-b)(c-a))-(b^3(c+a))/((b-c)(a-b))-(c^3(a+b))/((c-a)(b-c))a3(b+c)(ab)(ca)b3(c+a)(bc)(ab)c3(a+b)(ca)(bc)

or -(a^3(b+c)(b-c)+b^3(c+a)(c-a)+c^3(a+b)(a-b))/((a-b)(b-c)(c-a))a3(b+c)(bc)+b3(c+a)(ca)+c3(a+b)(ab)(ab)(bc)(ca)

or -(a^3(b^2-c^2)+b^3(c^2-a^2)+c^3(a^2-b^2))/((a-b)(b-c)(c-a))a3(b2c2)+b3(c2a2)+c3(a2b2)(ab)(bc)(ca)

or -(a^3(b^2-c^2)-a^2(b^3-c^3)+b^2c^2(b-c))/((a-b)(b-c)(c-a))a3(b2c2)a2(b3c3)+b2c2(bc)(ab)(bc)(ca)

or -((b-c)[(a^3(b+c)-a^2(b^2+bc+c^2)+b^2c^2]))/((a-b)(b-c)(c-a))(bc)[(a3(b+c)a2(b2+bc+c2)+b2c2])(ab)(bc)(ca)

or -((a^3b+a^3c-a^2b^2-a^2bc-a^2c^2+b^2c^2))/((a-b)(c-a))(a3b+a3ca2b2a2bca2c2+b2c2)(ab)(ca)

or -(c^2(b^2-a^2)+c(a^3-a^2b)+a^3b-a^2b^2)/((a-b)(c-a))c2(b2a2)+c(a3a2b)+a3ba2b2(ab)(ca)

or -(c^2(b-a)(b+a)+ca^2(a-b)+a^2b(a-b))/((a-b)(c-a))c2(ba)(b+a)+ca2(ab)+a2b(ab)(ab)(ca)

or -(-c^2(b+a)+ca^2+a^2b)/((c-a))c2(b+a)+ca2+a2b(ca)

or -(b(a^2-c^2)+ac(a-c))/((c-a))b(a2c2)+ac(ac)(ca)

or b(a+c)+acb(a+c)+ac

or ab+bc+caab+bc+ca