Add The Polynomials 5x³+2x²y-10x+16 And X³-4x²y+9-17

**Add the Polynomials 5x³+2x²y-10x+16 and x³-4x²y+9-17** ===========================================================

What is Polynomial Addition?

Polynomial addition is a mathematical operation that involves combining two or more polynomials by adding their corresponding terms. In this article, we will focus on adding two polynomials: 5x³+2x²y-10x+16 and x³-4x²y+9-17.

Step 1: Write the Polynomials

The first polynomial is 5x³+2x²y-10x+16, and the second polynomial is x³-4x²y+9-17. To add these polynomials, we need to write them in a vertical format, with the terms of each polynomial lined up.

  5x³ + 2x²y - 10x + 16
+ x³ - 4x²y + 9 - 17

Step 2: Add the Like Terms

Like terms are terms that have the same variable and exponent. In this case, we have two like terms: 5x³ and x³, and two like terms: 2x²y and -4x²y.

  5x³ + 2x²y - 10x + 16
+ x³ - 4x²y + 9 - 17
-------------------------
  (5x³ + x³) + (2x²y - 4x²y) + (-10x) + (16 + 9 - 17)

Step 3: Simplify the Expression

Now, we can simplify the expression by combining the like terms.

  (5x³ + x³) + (2x²y - 4x²y) + (-10x) + (16 + 9 - 17)
= 6x³ - 2x²y - 10x + 8

Q&A

Q: What is the final answer to the polynomial addition problem?

A: The final answer is 6x³ - 2x²y - 10x + 8.

Q: How do I add polynomials with different variables?

A: To add polynomials with different variables, you need to combine the like terms. If the variables are different, you cannot combine the terms.

Q: Can I add polynomials with negative coefficients?

A: Yes, you can add polynomials with negative coefficients. When adding polynomials with negative coefficients, you need to change the sign of the coefficient when combining like terms.

Q: How do I simplify a polynomial expression?

A: To simplify a polynomial expression, you need to combine the like terms. This involves adding or subtracting the coefficients of the like terms.

Q: What is the difference between adding and subtracting polynomials?

A: The difference between adding and subtracting polynomials is that when subtracting polynomials, you need to change the sign of the terms in the second polynomial.

Conclusion

In this article, we have discussed how to add polynomials, including writing the polynomials in a vertical format, adding like terms, and simplifying the expression. We have also answered some common questions about polynomial addition. By following these steps, you can add polynomials with ease and simplify complex expressions.

Common Mistakes to Avoid

When adding polynomials, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not combining like terms
• Changing the sign of the terms in the second polynomial when subtracting
• Not simplifying the expression after combining like terms

Tips and Tricks

Here are some tips and tricks to help you add polynomials:

• Use a vertical format to write the polynomials
• Combine like terms first
• Simplify the expression after combining like terms
• Check your work by plugging in values for the variables

By following these tips and tricks, you can add polynomials with ease and simplify complex expressions.