The Sum Of Two Polynomials Is 8 D 6 − 3 C 3 D 2 + 5 C 2 D 3 − 4 C D 4 + 9 8d^6 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 8 D 6 − 3 C 3 D 2 + 5 C 2 D 3 − 4 C D 4 + 9 . If One Addend Is 2 D 6 − C 3 D 2 + 8 C D 4 + 1 2d^6 - C^3d^2 + 8cd^4 + 1 2 D 6 − C 3 D 2 + 8 C D 4 + 1 , What Is The Other Addend?A. 6 D 6 − 2 C 3 D 2 + 5 C 2 D 3 − 12 C D 4 + 8 6d^6 - 2c^3d^2 + 5c^2d^3 - 12cd^4 + 8 6 D 6 − 2 C 3 D 2 + 5 C 2 D 3 − 12 C D 4 + 8 B. $6d^6 - 4c 3d 2 + 3c 2d 3 - 4cd^4 +

Understanding Polynomial Addition

When adding two polynomials, we combine like terms, which are terms that have the same variable and exponent. In this case, we are given the sum of two polynomials and one of the addends, and we need to find the other addend.

The Sum of Two Polynomials

The sum of two polynomials is given as:

$$8d^6 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9$$

One of the Addends

One of the addends is given as:

$$2d^6 - c^3d^2 + 8cd^4 + 1$$

Finding the Other Addend

To find the other addend, we need to subtract the given addend from the sum of the two polynomials. This can be done by combining like terms and simplifying the expression.

Step 1: Subtract the Given Addend

Subtract the given addend from the sum of the two polynomials:

$$\begin{array}{rcl} (8d^6 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9) - (2d^6 - c^3d^2 + 8cd^4 + 1) & = & \\ 8d^6 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - 2d^6 + c^3d^2 - 8cd^4 - 1 & = & \\ \end{array}$$

Step 2: Combine Like Terms

Combine like terms:

$$\begin{array}{rcl} (8d^6 - 2d^6) + (-3c^3d^2 + c^3d^2) + (5c^2d^3) + (-4cd^4 - 8cd^4) + (9 - 1) & = & \\ 6d^6 - 2c^3d^2 + 5c^2d^3 - 12cd^4 + 8 & = & \\ \end{array}$$

The Other Addend

The other addend is:

$$6d^6 - 2c^3d^2 + 5c^2d^3 - 12cd^4 + 8$$

Conclusion

In this article, we have shown how to find the other addend of a polynomial sum by subtracting one of the addends from the sum of the two polynomials. We have also demonstrated how to combine like terms and simplify the expression.

Final Answer

The final answer is:

$$6d^6 - 2c^3d^2 + 5c^2d^3 - 12cd^4 + 8$$

This is the other addend of the polynomial sum.

Discussion

This problem is a great example of how to apply the concept of polynomial addition to real-world problems. By understanding how to combine like terms and simplify expressions, we can solve complex problems in mathematics and other fields.

Related Problems

If you are interested in learning more about polynomial addition, you may want to try the following problems:

• Find the sum of the following two polynomials: $3x^2 + 2x - 1$ and $2x^2 - 3x + 4$
• Find the difference of the following two polynomials: $x^3 + 2x^2 - 3x + 1$ and $2x^3 - x^2 + 3x - 2$

These problems will help you practice your skills in polynomial addition and subtraction.

Conclusion

In conclusion, we have shown how to find the other addend of a polynomial sum by subtracting one of the addends from the sum of the two polynomials. We have also demonstrated how to combine like terms and simplify the expression. This problem is a great example of how to apply the concept of polynomial addition to real-world problems.

Understanding Polynomial Addition

Polynomial addition is a fundamental concept in algebra that involves combining like terms to simplify expressions. In this article, we will answer some frequently asked questions about polynomial addition.

Q: What is polynomial addition?

A: Polynomial addition is the process of combining like terms in two or more polynomials to simplify the resulting expression.

Q: How do I add polynomials?

A: To add polynomials, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

Q: What is the difference between polynomial addition and polynomial subtraction?

A: Polynomial addition involves combining like terms to simplify the resulting expression, while polynomial subtraction involves subtracting one polynomial from another. For example, if we have the polynomials $x^2 + 2x - 1$ and $2x^2 - 3x + 4$, we can add them by combining like terms: $(x^2 + 2x - 1) + (2x^2 - 3x + 4) = 3x^2 - x + 3$. On the other hand, if we want to subtract the second polynomial from the first, we would perform the following operation: $(x^2 + 2x - 1) - (2x^2 - 3x + 4) = -x^2 + 5x - 5$.

Q: Can I add polynomials with different variables?

A: No, you cannot add polynomials with different variables. For example, you cannot add the polynomials $x^2 + 2x - 1$ and $y^2 + 2y - 1$ because they have different variables ($x$ and $y$).

Q: Can I add polynomials with different exponents?

A: Yes, you can add polynomials with different exponents. For example, you can add the polynomials $x^2 + 2x - 1$ and $x^3 + 2x^2 - 1$ by combining like terms: $(x^2 + 2x - 1) + (x^3 + 2x^2 - 1) = x^3 + 4x^2 + 2x - 2$.

Q: How do I simplify a polynomial expression?

A: To simplify a polynomial expression, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, if we have the polynomial expression $x^2 + 2x^2 + 3x - 2x$, we can simplify it by combining like terms: $(x^2 + 2x^2) + (3x - 2x) = 3x^2 + x$.

Q: Can I add polynomials with coefficients?

A: Yes, you can add polynomials with coefficients. For example, you can add the polynomials $2x^2 + 3x - 1$ and $4x^2 + 2x + 1$ by combining like terms: $(2x^2 + 3x - 1) + (4x^2 + 2x + 1) = 6x^2 + 5x$.

Q: How do I subtract polynomials?

A: To subtract polynomials, you need to subtract each term of the second polynomial from the corresponding term of the first polynomial. For example, if we have the polynomials $x^2 + 2x - 1$ and $2x^2 - 3x + 4$, we can subtract the second polynomial from the first by performing the following operation: $(x^2 + 2x - 1) - (2x^2 - 3x + 4) = -x^2 + 5x - 5$.

Conclusion

In this article, we have answered some frequently asked questions about polynomial addition. We have covered topics such as combining like terms, adding polynomials with different variables and exponents, and simplifying polynomial expressions. We hope that this article has been helpful in understanding polynomial addition and will provide a solid foundation for further study in algebra.

Related Articles

If you are interested in learning more about polynomial addition, you may want to check out the following articles:

• Polynomial Addition: A Step-by-Step Guide
• Polynomial Subtraction: A Step-by-Step Guide
• Simplifying Polynomial Expressions: A Guide

These articles will provide you with a more in-depth understanding of polynomial addition and will help you to become proficient in simplifying polynomial expressions.

Practice Problems

If you are interested in practicing your skills in polynomial addition, you may want to try the following problems:

• Add the polynomials $x^2 + 2x - 1$ and $2x^2 - 3x + 4$
• Subtract the polynomial $2x^2 - 3x + 4$ from the polynomial $x^2 + 2x - 1$
• Simplify the polynomial expression $x^2 + 2x^2 + 3x - 2x$

These problems will help you to reinforce your understanding of polynomial addition and will provide you with a solid foundation for further study in algebra.