Simplify the given algebraic expression: $(5 x - 3) (x + 2) - (2 x + 5) (4 x - 3)$

3 x^{2} - 7 x + 9

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9 - 3 x^{2} - 7 x

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3 x^{2} + 7 x - 9

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- 3 x^{2} - 7 x - 9

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Solution

The correct option is B $9 - 3 x^{2} - 7 x$
$(5 x - 3) (x + 2) - (2 x + 5) (4 x - 3) = [5 x (x + 2) - 3 (x + 2)] - [2 x (4 x - 3) + 5 (4 x - 3)] = [5 x^{2} + 10 x - 3 x - 6] - [8 x^{2} - 6 x + 20 x - 15] = (5 x^{2} + 7 x - 6) - (8 x^{2} + 14 x - 15) = 5 x^{2} + 7 x - 6 - 8 x^{2} - 14 x + 15 = 5 x^{2} - 8 x^{2} + 7 x - 14 x - 6 + 15 = - 3 x^{2} - 7 x + 9 = 9 - 3 x^{2} - 7 x$

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