Let's simplify the expression [tex]\(1 x^4 + 2 x y \cdot x^4 - 4 x y^3\)[/tex] step-by-step.
1. Start with the initial expression:
[tex]\[
1 x^4 + 2 x y \cdot x^4 - 4 x y^3
\][/tex]
2. Simplify each term separately:
- The first term is [tex]\(1 x^4\)[/tex], which simplifies to [tex]\(x^4\)[/tex].
- The second term is [tex]\(2 x y \cdot x^4\)[/tex]. Since [tex]\(x \cdot x^4 = x^5\)[/tex], this simplifies to [tex]\(2 x^5 y\)[/tex].
- The third term is already in its simplest form: [tex]\(-4 x y^3\)[/tex].
3. Combine the simplified terms:
[tex]\[
x^4 + 2 x^5 y - 4 x y^3
\][/tex]
Thus, the simplified form of the expression [tex]\(1 x^4 + 2 x y \cdot x^4 - 4 x y^3\)[/tex] is:
[tex]\[
2 x^5 y + x^4 - 4 x y^3
\][/tex]
