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Addition and Subtraction of Algebraic Expression

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Question

Simplify the polynomial and write it in standard form:
$(- 2 x - 5) (2 x - 8) - (2 x - 5) (3 x + 7)$

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Solution

$(- 2 x - 5) (2 x - 8) - (2 x - 5) (3 x + 7)$
$= - 4 x^{2} + 16 x - 10 x + 40 - 6 x^{2} - 14 x + 15 x + 35$
$= - 4 x^{2} - 6 x^{2} + 16 x - 10 x - 14 x + 15 x + 40 + 35$
$= - 10 x^{2} + 17 x + 75$
Ans $= - 10 x^{2} + 17 x + 75$

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