Question

A=x+y b=x-y c=x+2y . find the value of a2+b2+c2-ab-bc-ca

Answer 1

Answer:

The value of $a^{2}+b^{2}+c^{2}-ab-bc-ca$ is $7y^{2}$.

Step-by-step explanation:

It is provided that:

$a=x+y\\b=x-y\\c=c+2y$

Compute the value of $a^{2}+b^{2}+c^{2}-ab-bc-ca$ as follows:

$a^{2}+b^{2}+c^{2}-ab-bc-ca=(x+y)^{2}+(x-y)^{2}+(x+2y)^{2}-(x+y)(x-y)-(x-y)(x+2y)-(x+2y)(x+y)\\=x^{2}+y^{2}+2xy+x^{2}+y^{2}-2xy+x^{2}+4y^{2}+4xy-x^{2}+y^{2} -x^{2}-xy+2y^{2}-x^{2}-3xy-2y^{2}\\=7y^{2}$

Thus, the value of $a^{2}+b^{2}+c^{2}-ab-bc-ca$ is $7y^{2}$.