Let's solve the problem by identifying like terms and combining them step-by-step.
Step 1: Write down the original expression.
The given expression is:
[tex]\[ 10x^2y + 2xy^2 - 4x^2 - 4x^2y \][/tex]
Step 2: Group the like terms.
To combine the terms, identify and group the coefficients of the same variables:
- [tex]\(10x^2y\)[/tex] and [tex]\(-4x^2y\)[/tex] are like terms because they both contain [tex]\(x^2y\)[/tex].
- [tex]\(2xy^2\)[/tex] does not have any like terms.
- [tex]\(-4x^2\)[/tex] does not have any like terms.
Step 3: Combine the like terms.
- For [tex]\(x^2y\)[/tex]: Combine [tex]\(10x^2y\)[/tex] and [tex]\(-4x^2y\)[/tex]:
[tex]\[ 10x^2y - 4x^2y = 6x^2y \][/tex]
So, the expression becomes:
[tex]\[ 6x^2y + 2xy^2 - 4x^2 \][/tex]
Step 4: Write the expression with like terms grouped together.
The correct expression with the terms grouped is:
[tex]\[ -4x^2 + 2xy^2 + 6x^2y \][/tex]
Now, let's match this final expression to one of the provided options:
- [tex]\(\left(-4 x^2\right)+2 x y^2+\left[10 x^2 y+\left(-4 x^2 y\right)\right]\)[/tex]
This matches the expression we derived.
So, the correct option is:
[tex]\[ \left(-4 x^2\right)+2 x y^2+\left[10 x^2 y+\left(-4 x^2 y\right)\right] \][/tex]
