Question

Subtract these polynomials.
(2x^2 +4x+3) -(4x^2-2x-3) =

Answer 1

To subtract the polynomials \( (2x^2 + 4x + 3) - (4x^2 - 2x - 3) \), we can distribute the negative sign across the second polynomial and then combine like terms.

Starting with the expression:

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

Distributing the negative sign:

\[
= 2x^2 + 4x + 3 - 4x^2 + 2x + 3
\]

Now, combine like terms:

1. For \(x^2\) terms: \(2x^2 - 4x^2 = -2x^2\)
2. For \(x\) terms: \(4x + 2x = 6x\)
3. For constant terms: \(3 + 3 = 6\)

Putting it all together, we have:

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

Thus, the result of the subtraction is:

\[
\boxed{-2x^2 + 6x + 6}
\]