Question

(a+b-c)² = a²+b²+ c² + 2ab-2bc-2ca do the derivation ​

Answer 1

Answer

We just read that by multiplying (a + b + c) by itself we can easily derive the a2 + b2 + c2 formula. Let us see the expansion of a2 + b2 + c2 formula.

(a + b + c)2 = (a + b + c)(a + b + c)

(a + b + c)2 = a2 + ab + ac + ab + b2 + bc + ca + bc + c2

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

On subtracting 2ab + 2bc + 2ca from both sides of the above formula, the a2 + b2 + c2 formula is:

a2 + b2 + c2 = (a + b + c)2 - 2 (ab + bc + ca)

(or)

a2 + b2 + c2 = (a + b + c)2 - 2ab - 2bc - 2ca

a2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca)

We can also express a2 + b2 + c2 formula as,

a2 + b2 + c2 = (a - b - c)2 + 2ab + 2ac - 2bc

Let us see how to use the a2 + b2 + c2 formula in the following section.

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Answer 2

The answer is in the photo