To find the sum of the polynomials and group the like terms together for the given expression:
[tex]\[ 10x^2y + 2xy^2 - 4x^2 - 4x^2y \][/tex]
we need to follow these steps:
1. Identify and group the like terms from the given polynomial expression.
Like Terms Identification:
- For the terms involving \(x^2y\):
[tex]\[ 10x^2y \,\,\, \text{and} \,\,\, -4x^2y \][/tex]
- For the terms involving \(xy^2\):
[tex]\[ 2xy^2 \][/tex]
- For the terms involving \(x^2\):
[tex]\[ -4x^2 \][/tex]
2. Combine the like terms.
Combining Like Terms:
- Combine the \(x^2y\) terms:
[tex]\[ 10x^2y - 4x^2y = 6x^2y \][/tex]
- There is only one \(xy^2\) term:
[tex]\[ 2xy^2 \][/tex]
- And only one \(x^2\) term:
[tex]\[ -4x^2 \][/tex]
3. Write the combined and grouped expression:
[tex]\[ (-4x^2) + 2xy^2 + [6x^2y] \][/tex]
Thus, the expression showing the sum of the polynomials with like terms grouped together is:
[tex]\[ \left(-4x^2\right) + 2xy^2 + \left[6x^2y\right] \][/tex]
So, the answer is:
[tex]\[ \left(-4x^2\right)+2xy^2+\left[10x^2y+\left(-4x^2y\right)\right] \][/tex]
