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Simplify the following :
$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$
Given :
The given expression is $( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$.
To do :
We have to simplify the given expression.
Solution :
$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$
$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4) = x.( 3 x^2 + 5 x - 7 )-1.( 3 x^2 + 5 x - 7 ) - x.( x^2 - 2 x + 3 ) - 4( x^2 - 2 x + 3 )$
$= 3 x^3 + 5 x^2 -7x - 3 x^2 - 5 x + 7- x^3 + 2 x^2 - 3 x - 4 x^2 + 8 x -12$
$ = (3-1) x^3 + (5-3+2-4) x^2 + (-7-5-3+8) x + (7-12)$
$ = 2x^3 + 0.x^2 - 7 x - 5.$
$= 2x^3 - 7 x - 5$.
The simplified form of $( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$ is $ 2x^3 - 7 x - 5$.
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