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Which of the following is the factorized form of the polynomial $a (a + b - c) - b c$ ?

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(a + c) (a + b)

(a - c) (a - b)

(a + c) (a - b)

(a - c) (a + b)

answer is D.

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Detailed Solution

The given polynomial is

a (a + b - c) - b c .

We will evaluate the given polynomial and then arrange the like terms together.
Thus, the given polynomial can be written as,

a (a + b - c) - b c = a^{2} + a b - a c - b c

Now, on taking out the common terms, we get,

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

Hence, the given polynomial

a (a + b - c) - b c

is factorized as

(a - c) (a + b) .

Thus, option (4) is correct.

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