Question

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

Answer 1

Step-by-step explanation:

this is the correct answer I hope that you can understand

Answer 2

Given,

(a+b+c)² = a² + b² + c²+ 2(ab+bc+ca)

Here L.H.S.(Left Hand Side) is (a+b+c)² and R.H.S. is [a² + b² + c²+ 2(ab+bc+ca)].

Now, solve for RHS,

a² + b² + c²+ 2(ab+bc+ca)

= a²+b²+c²+2ab+2bc+2ca. ____ (1).

Now, solve for LHS,

(a+b+c)²

= (a+b+c)×(a+b+c)

= a(a+b+c) + b(a+b+c) + c(a+b+c) [now, solve for each bracket]

= [a² + ab + ac] + [ba + b² + bc] + [ca + cb + c²]

[Now, open all brackets and solve for the final value]

= a² + ab + ac + ba + b² + bc + ca + cb + c²

[Now re-arrange the polynomial]

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

[ ba, becomes ab and ca becomes ac and cb becomes bc]

= a² + b² + c² + 2ab + 2ab + 2ac [after adding the like terms you will get this]

Hope this helps.......