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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Updated on: 10-Oct-2022

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