Simplify: ${(3 x^{2} - 6 x + 5) + (2 x - 2 x^{2} + 5)} - (x^{2} - 4 x + 10)$

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Solution

Let us solve the given expression $[(3 x^{2} - 6 x + 5) + (2 x - 2 x^{2} + 5)] - (x^{2} - 4 x + 10)$ as shown below:

$[(3 x^{2} - 6 x + 5) + (2 x - 2 x^{2} + 5)] - (x^{2} - 4 x + 10) = (3 x^{2} - 6 x + 5 + 2 x - 2 x^{2} + 5) - (x^{2} - 4 x + 10) = [(3 x^{2} - 2 x^{2}) + (- 6 x + 2 x) + (5 + 5)] - (x^{2} - 4 x + 10) (C o m b i n i n g l i k e t e r m s) = [(3 - 2) x^{2} + (- 6 + 2) x + 10] - (x^{2} - 4 x + 10) = (x^{2} - 4 x + 10) - (x^{2} - 4 x + 10) = 0$

Hence, $[(3 x^{2} - 6 x + 5) + (2 x - 2 x^{2} + 5)] - (x^{2} - 4 x + 10) = 0$ .

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