Question

Subtract the polynomial expressions and simplify completely.
(3x5+7x2−4x+8)−(4x4+8x2−3x+7)
(1 point)

Answer 1

To subtract the polynomial expressions \( (3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7) \), we need to distribute the negative sign across the second expression and combine like terms.

Starting with the given expression:

\[
(3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7)
\]

Distributing the negative sign:

\[
= 3x^5 + 7x^2 - 4x + 8 - 4x^4 - 8x^2 + 3x - 7
\]

Now, we can combine like terms:

1. For \( x^5 \): \( 3x^5 \)
2. For \( x^4 \): \( -4x^4 \)
3. For \( x^2 \): \( 7x^2 - 8x^2 = -1x^2 \) (or \(-x^2\))
4. For \( x \): \( -4x + 3x = -1x \) (or \(-x\))
5. Constant terms: \( 8 - 7 = 1 \)

Putting it all together, we get:

\[
3x^5 - 4x^4 - x^2 - x + 1
\]

Thus, the simplified result of the subtraction is:

\[
\boxed{3x^5 - 4x^4 - x^2 - x + 1}
\]