Simplify:
$(x^3 - 2x^2 + 3x - 4) (x - 1) - (2x - 3) (x^2 - x + 1)$
Given:
$(x^3 - 2x^2 + 3x - 4) (x - 1) - (2x - 3) (x^2 - x + 1)$
To do:
We have to simplify the given expression.
Solution:
$(x^3 - 2x^2 + 3x - 4) (x - 1) - (2x - 3) (x^2 - x + 1)=[x(x^3 - 2x^2 + 3x - 4) - 1 (x^3 - 2x^2 + 3x - 4)] - [2x (x^2 - x + 1) - 3 (x^2 - x + 1)]$
$= [x^4 - 2x^3 + 3x^2 - 4x - x^3 + 2x^2 - 3x + 4]-[2x^3 - 2x^2 + 2x - 3x^2 + 3x - 3]$
$= (x^4 - 2x^3 - x^3 + 3x^2 + 2x^2 - 4x - 3x + 4)-(2x^3 - 2x^2 - 3x^2 + 2x + 3x - 3)$
$= (x^4 - 3x^3 + 5x^2 - 7x + 4) - (2x^3 - 5x^2 + 5x - 3)$
$= x^4 - 3x^3 + 5x^2 - 7x + 4 - 2x^3 + 5x^2 - 5x + 3$
$= x^4 - 3x^3 - 2x^3 + 5x^2 + 5x^2 - 7x - 5x + 4 + 3$
$= x^4 - 5x^3 + 10x^2 - 12x + 7$
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