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Question

Derive the following identity: (xa)(xb)=x2x(a+b)+ab

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Solution

(xa)(xb)=x2x(a+b)+ab
First take L.H.S
(xa)(xb)
To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.
= x.xx.ba.x+a.b
= x2x(a+b)+ab
So, L.H.S = R.H.S
x2x(a+b)+ab=x2x(a+b)+ab

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