Question

Subtract the sum of 2x − x² + 5 and − 4x − 3 + 7x² from 5.

Answer 1

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 \[3 + 2x - 6 x^2\].