To solve the expression [tex]\(\left(3x^2 + 2xy + 7\right) - \left(6x^2 - 4xy + 3\right)\)[/tex], follow these steps:
1. Distribute the Negative Sign:
Distribute the negative sign through the second expression:
[tex]\[
3x^2 + 2xy + 7 - (6x^2 - 4xy + 3) = 3x^2 + 2xy + 7 - 6x^2 + 4xy - 3
\][/tex]
2. Combine Like Terms:
Combine the like terms, i.e., those involving [tex]\(x^2\)[/tex], [tex]\(xy\)[/tex], and constants.
- For the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 - 6x^2 = -3x^2\)[/tex]
- For the [tex]\(xy\)[/tex] terms: [tex]\(2xy + 4xy = 6xy\)[/tex]
- For the constant terms: [tex]\(7 - 3 = 4\)[/tex]
3. Write the Simplified Expression:
Combine the results to get the simplified expression:
[tex]\[
-3x^2 + 6xy + 4
\][/tex]
Thus, the expression [tex]\(\left(3x^2 + 2xy + 7\right) - \left(6x^2 - 4xy + 3\right)\)[/tex] simplifies to:
[tex]\(\boxed{-3x^2 + 6xy + 4}\)[/tex]
Looking at the given options, the correct choice is:
3) [tex]\(-3x^2 + 6xy + 4\)[/tex]
