Certainly! Let's simplify the expression [tex]\(2 x^2 y + x y + 3 x y - x^2 y\)[/tex] step-by-step.
1. Rewrite the expression with like terms grouped together:
[tex]\[
2 x^2 y - x^2 y + x y + 3 x y
\][/tex]
2. Combine the like terms:
- For the [tex]\(x^2 y\)[/tex] terms: [tex]\(2 x^2 y - x^2 y = (2 - 1) x^2 y = x^2 y\)[/tex]
- For the [tex]\(x y\)[/tex] terms: [tex]\(x y + 3 x y = (1 + 3) x y = 4 x y\)[/tex]
Now the expression is:
[tex]\[
x^2 y + 4 x y
\][/tex]
3. Factor out the common term [tex]\(x y\)[/tex] from both terms:
[tex]\[
x y (x + 4)
\][/tex]
Thus, the simplified expression is:
[tex]\[
x y (x + 4)
\][/tex]
So, [tex]\(2 x^2 y + x y + 3 x y - x^2 y\)[/tex] simplifies to [tex]\(x y (x + 4)\)[/tex].
