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Addition and Subtraction of Algebraic Expression

By how much d...

Question

By how much does $x^{2} - 2 a x + 5$ exceed $3 x^{2} - 5 x + 6$ ?

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Solution

Required solution $= 3 x^{2} - 5 x + 6 - (x^{2} - 2 a x + 5)$
$= 2 x^{2} - (5 + 2 a) x + 1$
$∴ x^{2} - 2 a x + 5$ exceeds $3 x^{2} - 5 x + 6$ by $2 x^{2} - (5 + 2 a) x + 1$

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