SOLUTION: Prove these identities. a) (a+b+c)(ab+bc+ca)−abc= (a+b)(b+c)(c+a) b) (ax+by)^2 + (ay−bx)^2 +c^2(x^2 +y^2)= (x^2 +y^2)(a^2 +b^2 +c^2) Thank you so much :)

SOLUTION: Prove these identities. a) (a+b+c)(ab+bc+ca)−abc= (a+b)(b+c)(c+a) b) (ax+by)^2 + (ay−bx)^2 +c^2(x^2 +y^2)= (x^2 +y^2)(a^2 +b^2 +c^2) Thank you so much :)

Algebra.Com

Question 1139327: Prove these identities.
a) (a+b+c)(ab+bc+ca)−abc= (a+b)(b+c)(c+a)
b) (ax+by)^2 + (ay−bx)^2 +c^2(x^2 +y^2)= (x^2 +y^2)(a^2 +b^2 +c^2)
Thank you so much :)
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
a)

manipulate left side

=
= ...group
=

=
=
=
=
=

b.)

manipulate left side:

=
=
=
=

RELATED QUESTIONS
ab(x^2+y^2)-xy(a^2+b^2) ab+bc+ax+cx a(a+b-c)-bc (answered by richwmiller)

can you please help me to factorize the following 1. a^2(b+c)+b^2(c+a)+c^2(a+b)+2abc (answered by khwang)

If a,b,c are in G.P. Then prove that... (answered by Edwin McCravy)

If a^x=bc;b^y=ca;c^z=ab then prove x/(x+1) + y/(y+1) + z/(z+1)... (answered by Edwin McCravy)

If (a+b)^2 + (b+c)^2 + (c+d)^2 = 4(ab+bc+cd), prove... (answered by mananth)

Solve for x, {{{((a-x)/(a-b))-2=(c-x)/(b-c)}}}. Here's my working, if you could correct... (answered by god2012,nerdybill)

express as a rational expression... (answered by Lauren61292)

if {{{(bx - ay)/b = (cy - bz)/c = (az - cx)/a}}} and given that {{{bx!=ay}}}... (answered by Edwin McCravy)

Let a,b,c be positive reals. Find the minimum value of... (answered by Collinwilfixyouuprealnice)