Simplify:
Question:

Simplify:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)

Solution:

To simplify,we will proceed as follows:

(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)

$=\left[\left(x^{3}-2 x^{2}+3 x-4\right)(x-1)\right]-\left[(2 x-3)\left(x^{2}-x+1\right)\right]$

$=\left[x\left(x^{3}-2 x^{2}+3 x-4\right)-1\left(x^{3}-2 x^{2}+3 x-4\right)\right]-\left[2 x\left(x^{2}-x+1\right)-3\left(x^{2}-x+1\right)\right]$      (Distributive law)

$=\left[x\left(x^{3}-2 x^{2}+3 x-4\right)-1\left(x^{3}-2 x^{2}+3 x-4\right)\right]-\left[2 x\left(x^{2}-x+1\right)-3\left(x^{2}-x+1\right)\right]$ 

=x^{4}-2 x^{3}+3 x^{2}-4 x-x^{3}+2 x^{2}-3 x+4-\left[2 x^{3}-2 x^{2}+2 x-3 x^{2}+3 x-3\right]

$=x^{4}-2 x^{3}+3 x^{2}-4 x-x^{3}+2 x^{2}-3 x+4-2 x^{3}+2 x^{2}-2 x+3 x^{2}-3 x+3$

$=x^{4}-2 x^{3}-2 x^{3}-x^{3}+3 x^{2}+2 x^{2}+2 x^{2}+3 x^{2}-4 x-3 x-2 x-3 x+4+3 \quad$ (Rearranging)

$=x^{4}-5 x^{3}+10 x^{2}-12 x+7 \quad$ (Combining like terms)

Thus, the answer is $x^{4}-5 x^{3}+10 x^{2}-12 x+7$.

 

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