Question

Prove the following:(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Taking LHS of the identity:

(a + b +c)2

This can also be written as:

= (a + b + c) (a + b + c)

Multiply as we do multiplication of trinomials and we get:

= a(a + b + c) + b(a + b + c) + c(a + b + c)

= a2 + ab + ac + ab + b2 + bc + ac + bc + c2

Rearrange the terms and we get:

= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac

Add like terms and we get:

= a2 + b2+ c2 + 2ab + 2bc + 2ca

Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

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