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Question
Subtract the sum of 2x − x2 + 5 and − 4x − 3 + 7x2 from 5.
Solution
We have to subtract the sum of (2x − x2 + 5) and (− 4x − 3 + 7x) from 5.
\[5 - \left\{ \left( 2x - x^2 + 5 \right) + \left( - 4x - 3 + 7 x^2 \right) \right\}\]
\[ = 5 - \left( 2x - 4x - x^2 + 7 x^2 + 5 - 3 \right)\]
\[ = 5 - 2x + 4x + x^2 - 7 x^2 - 5 + 3\]
\[= 5 - 5 + 3 - 2x + 4x + x^2 - 7 x^2\] (Collecting like terms)
\[= 3 + 2x - 6 x^2\] (Combining like terms)
Thus, the answer is \[3 + 2x - 6 x^2\].
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