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Addition and Subtraction of Algebraic Expression

Simplify:x2-3...

Question

Simplify:
(x² − 3x + 2)(5x − 2) − (3x² + 4x − 5)(2x − 1)

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Solution

To simplify, we will proceed as follows:

$(x^{2} - 3 x + 2) (5 x - 2) - (3 x^{2} + 4 x - 5) (2 x - 1) = [(x^{2} - 3 x + 2) (5 x - 2)] - [(3 x^{2} + 4 x - 5) (2 x - 1)]$
$= [5 x (x^{2} - 3 x + 2) - 2 (x^{2} - 3 x + 2)] - [2 x (3 x^{2} + 4 x - 5) - 1 \times (3 x^{2} + 4 x - 5)]$ (Distributive law)
$= [5 x^{3} - 15 x^{2} + 10 x - (2 x^{2} - 6 x + 4)] - [6 x^{3} + 8 x^{2} - 10 x - 3 x^{2} - 4 x + 5] = [5 x^{3} - 15 x^{2} + 10 x - 2 x^{2} + 6 x - 4] - [6 x^{3} + 8 x^{2} - 10 x - 3 x^{2} - 4 x + 5] = 5 x^{3} - 15 x^{2} + 10 x - 2 x^{2} + 6 x - 4 - 6 x^{3} - 8 x^{2} + 10 x + 3 x^{2} + 4 x - 5$
$= 5 x^{3} - 6 x^{3} - 15 x^{2} - 2 x^{2} - 8 x^{2} + 3 x^{2} + 10 x + 6 x + 10 x + 4 x - 5 - 4$ (Rearranging)
$= - x^{3} - 22 x^{2} + 30 x - 9$ (Combining like terms)

Thus, the answer is $- x^{3} - 22 x^{2} + 30 x - 9$ .

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