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The completely factored form of the expression $a b^{2} - b c^{2} - a b + c^{2}$ is [[1]].

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answer is B − 1 A B − C 2.

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Detailed Solution

The completely factored form of the expression

a b^{2} - b c^{2} - a b + c^{2}

(b - 1) (a b - c^{2})

.
The given expression is as follows,

a b^{2} - b c^{2} - a b + c^{2}

.
It can be observed that there are four terms in the above expression. So, to factorize it, we first need to regroup the terms with common factors, and then we need to perform the factorization.

a b^{2} - b c^{2} - a b + c^{2} \Leftrightarrow (a b^{2} - b c^{2}) + (- a b + c^{2})

Now, we need to factor out the highest common factor from each group to get the completely factored form of the expression as follows,

a b (b - 1) - c^{2} (b - 1) = (b - 1) (a b - c^{2})

So, it can be observed that the expression

(b - 1) (a b - c^{2})

can’t be factorized any further.
Hence, it is the completely factored form of the given polynomial expression.

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