The factored form of the polynomial expression $x^{3} (2 a - b) + x^{2} (2 a - b)$ is [[1]].

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answer is X X + 1 2 A − B.

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Detailed Solution

The factored form of the polynomial expression

x^{3} (2 a - b) + x^{2} (2 a - b)

x (x + 1) (2 a - b)

.
To find the factors of this expression, we use the method of common factors.
In the given expression, it can be clearly observed that the binomial term

(2 a - b)

is appearing twice.
Now, factoring out

(2 a - b)

, the polynomial expression can be written as follows,

(x^{3} + x^{2}) (2 a - b)

Again, it can be observed that the monomial term

x

can be again factored out from the term

(x^{3} + x^{2})

x (x + 1) (2 a - b)

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