Derive the following identity: $(x - a) (x - b) = x^{2} - x (a + b) + a b$

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Solution

$(x - a) (x - b) = x^{2} - x (a + b) + a b$
First take L.H.S
$(x - a) (x - b)$
To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.
$=$ $x . x - x . b - a . x + a . b$
$=$ $x^{2} - x (a + b) + a b$
So, L.H.S = R.H.S
$x^{2} - x (a + b) + a b = x^{2} - x (a + b) + a b$

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