Certainly! Let's solve the expression step by step.
We need to subtract the second expression from the first expression:
[tex]\[
\left(5 x^2 y^2 - 6 x y - 4 x y^2\right) - \left(2 x^2 y^2 + 4 x y - 5 + 6 y^2\right)
\][/tex]
Step 1: Distribute the negative sign across the terms in the second expression:
[tex]\[
5 x^2 y^2 - 6 x y - 4 x y^2 - 2 x^2 y^2 - 4 x y + 5 - 6 y^2
\][/tex]
Step 2: Combine like terms one by one:
- Combine [tex]\(x^2 y^2\)[/tex] terms:
[tex]\[
5 x^2 y^2 - 2 x^2 y^2 = 3 x^2 y^2
\][/tex]
- Combine [tex]\(x y\)[/tex] terms:
[tex]\[
-6 x y - 4 x y = -10 x y
\][/tex]
- Combine [tex]\(x y^2\)[/tex] terms:
[tex]\[
-4 x y^2 \quad \text{(nothing to combine with here)}
\][/tex]
- Combine [tex]\(y^2\)[/tex] terms:
[tex]\[
-6 y^2 \quad \text{(again, nothing to combine with)}
\][/tex]
- Combine the constant term:
[tex]\[
+5 \quad \text{(again, nothing to combine with)}
\][/tex]
Step 3: Put it all together:
[tex]\[
3 x^2 y^2 - 4 x y^2 - 10 x y - 6 y^2 + 5
\][/tex]
So, the simplified result of the original expression is:
[tex]\[
3 x^2 y^2 - 4 x y^2 - 10 x y - 6 y^2 + 5
\][/tex]
