Question

Subtract the polynomial expressions and simplify completely. (3x^5+7x^2-4x+8)-(4x^4+8x^2-3x+7)

Answer 1

To subtract the polynomial expressions \( (3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7) \), we first rewrite the expression by distributing the negative sign to the second polynomial:

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

Next, we combine like terms. We will arrange the terms by their degree:

1. The \( x^5 \) term:
- \( 3x^5 \)

2. The \( x^4 \) term:
- \( -4x^4 \)

3. The \( x^2 \) terms:
- \( 7x^2 - 8x^2 = -x^2 \)

4. The \( x \) terms:
- \( -4x + 3x = -x \)

5. The constant terms:
- \( 8 - 7 = 1 \)

Now, we can combine all of the simplified terms:

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

Thus, the simplified expression is:

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