Solve :- $(3 x^{2} + 5 x - 7) (x - 1) - (x^{2} - 2 x + 3) (x + 4)$

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Solution

$(3 x^{2} + 5 x - 7) (x - 1) - (x^{2} - 2 x + 3) (x + 4)$
$= x (3 x^{2} + 5 x - 7) - 1 (3 x^{2} + 5 x - 7) - x (x^{2} - 2 x + 3) - 4 (x^{2} - 2 x + 3)$
$= 3 x^{3} + 5 x^{2} - 7 x - 3 x^{2} - 5 x + 7 - x^{3} + 2 x^{2} - 3 x - 4 x^{2} + 8 x - 12$
$= 3 x^{3} - x^{3} + 5 x^{2} - 3 x^{2} + 2 x^{2} - 4 x^{2} - 7 x - 5 x - 3 x + 8 x - 12 + 7$
$= (3 - 1) x^{3} + (5 - 3 + 2 - 4) x^{2} + (- 7 - 5 - 3 + 8) x - 12 + 7$
$= 2 x^{3} + 0 x^{2} - 7 x - 5$
$= 2 x^{3} - 7 x - 5$

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