Certainly! Let's work through the expression [tex]\(4a + 2x^2 - 5x^4\)[/tex] step-by-step.
1. Identify the terms: The given expression consists of three terms: [tex]\(4a\)[/tex], [tex]\(2x^2\)[/tex], and [tex]\(-5x^4\)[/tex].
2. Understand the coefficients: Each term has a coefficient and a variable.
- In the term [tex]\(4a\)[/tex], the coefficient is 4 and the variable is [tex]\(a\)[/tex].
- In the term [tex]\(2x^2\)[/tex], the coefficient is 2 and the variable is [tex]\(x\)[/tex], which is raised to the power of 2.
- In the term [tex]\(-5x^4\)[/tex], the coefficient is -5 and the variable is [tex]\(x\)[/tex], which is raised to the power of 4.
3. Combine the terms: Since the terms involve different powers of [tex]\(x\)[/tex] and a different variable [tex]\(a\)[/tex], they cannot be combined or simplified further. Each term is distinct in its contribution to the overall expression:
- [tex]\(4a\)[/tex] remains as is because it is solely dependent on the variable [tex]\(a\)[/tex].
- [tex]\(2x^2\)[/tex] remains as is as it involves [tex]\(x\)[/tex] raised to the power of 2.
- [tex]\(-5x^4\)[/tex] remains as is as it involves [tex]\(x\)[/tex] raised to the power of 4.
4. Write the final expression: Putting it all together, the simplified form of the expression is:
[tex]\[ 4a - 5x^4 + 2x^2 \][/tex]
So the final, simplified expression is:
[tex]\[ 4a - 5x^4 + 2x^2 \][/tex]
This expression represents a polynomial with three terms, each contributing differently based on the variables and their respective coefficients and powers.
