Sure, let's break down the polynomial expression [tex]\(2x^6 - y^6\)[/tex] step-by-step to ensure we fully understand each part:
1. Identify the Terms:
- The expression consists of two terms: [tex]\(2x^6\)[/tex] and [tex]\(-y^6\)[/tex].
2. Understand the Coefficients and Exponents:
- In the term [tex]\(2x^6\)[/tex], the coefficient is 2, and the exponent of [tex]\(x\)[/tex] is 6. This means [tex]\(x\)[/tex] is raised to the power of 6 and then multiplied by 2.
- In the term [tex]\(-y^6\)[/tex], the coefficient is -1 (implicitly) and the exponent of [tex]\(y\)[/tex] is 6. This means [tex]\(y\)[/tex] is raised to the power of 6 and then multiplied by -1.
3. Combine the Terms:
- Since the terms include different variables raised to the same power, they cannot be simplified further through addition or subtraction. The expression remains in its polynomial form.
In conclusion, the polynomial expression [tex]\(2x^6 - y^6\)[/tex] consists of two terms that cannot be simplified further without additional context or specific values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. The expression is already in its simplest form.
