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Addition and Subtraction of Algebraic Expression

Subtract the ...

Question

Subtract the sum of $2 x^{2} - 4 x + 11$ and $7 x^{2} - 4 x + 1$ from the sum of $8 x^{2} - 7 x - 7$ and $6 x^{2} + 4 x - 6.$

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Solution

Let $S_{1} = (2 x^{2} - 4 x + 11) + (7 x^{2} - 4 x + 1) = (2 + 7) x^{2} + (- 4 - 4) x + (11 + 1) = 9 x^{2} - 8 x + 12$

and $S_{2} = (8 x^{2} - 7 x - 7) + (6 x^{2} + 4 x - 6) = (14) x^{2} + (- 7 + 4) x + (- 6 - 7) = 14 x^{2} - 3 x - 13$

Now, $S_{2} - S_{1} = (14 x^{2} - 3 x - 13) - (9 x^{2} - 8 x + 12) = 14 x^{2} - 3 x - 13 - 9 x^{2} + 8 x - 12 = 5 x^{2} + 5 x - 25$

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