Certainly! Let's simplify the given expression step-by-step.
We start with the given expression:
[tex]\[
(5x - xy^2) - (4xy^2 - 2x)
\][/tex]
First, we distribute the negative sign through the second expression:
[tex]\[
5x - xy^2 - 4xy^2 + 2x
\][/tex]
Next, we combine like terms. The terms involving [tex]\(x\)[/tex] are [tex]\(5x\)[/tex] and [tex]\(2x\)[/tex], and the terms involving [tex]\(xy^2\)[/tex] are [tex]\(-xy^2\)[/tex] and [tex]\(-4xy^2\)[/tex]:
[tex]\[
(5x + 2x) + (-xy^2 - 4xy^2)
\][/tex]
Simplify the coefficients:
[tex]\[
7x - 5xy^2
\][/tex]
Thus, the simplified form of the expression is:
[tex]\[
7x - 5xy^2
\][/tex]
Alternatively, we can factor out the common term [tex]\(x\)[/tex]:
[tex]\[
x(7 - 5y^2)
\][/tex]
Hence, the simplified result is equivalently written as:
[tex]\[
7x - 5xy^2 \quad \text{or} \quad x(7 - 5y^2)
\][/tex]
