Jennifer Is Rewriting A Polynomial By Combining Like Terms. Which Terms Does She Still Need To Combine To Finish Rewriting The Polynomial?${ 4c^2d - 7c 2d 2 + 3d^2 + C 2d 2 - 4cd^2 - C^2 }$Select All The Correct Locations On The Image.

Understanding Like Terms

In mathematics, like terms are terms that have the same variable(s) raised to the same power. When rewriting a polynomial, combining like terms is an essential step to simplify the expression. In this article, we will explore how to identify like terms and combine them to finish rewriting a polynomial.

The Given Polynomial

The given polynomial is:

${ 4c^2d - 7c^2d^2 + 3d^2 + c^2d^2 - 4cd^2 - c^2 }$

Identifying Like Terms

To identify like terms, we need to look for terms that have the same variable(s) raised to the same power. In the given polynomial, we can see that there are several terms that have the same variable(s) raised to the same power.

Terms with the Same Variable(s) Raised to the Same Power

• c^2d: This term appears twice in the polynomial, once with a coefficient of 4 and once with a coefficient of -1 (implied by the term -c^2d).
• c^2d2: This term appears twice in the polynomial, once with a coefficient of -7 and once with a coefficient of 1 (implied by the term c^2d2).
• d^2: This term appears once in the polynomial with a coefficient of 3.

Terms with Different Variable(s) Raised to Different Powers

• cd^2: This term appears once in the polynomial with a coefficient of -4.
• c^2: This term appears once in the polynomial with a coefficient of -1 (implied by the term -c^2).

Combining Like Terms

Now that we have identified the like terms, we can combine them to simplify the polynomial.

Combining c^2d Terms

The terms with the variable(s) c^2d are:

• 4c^2d
• -c^2d

We can combine these terms by adding their coefficients:

4c^2d - c^2d = 3c^2d

Combining c^2d2 Terms

The terms with the variable(s) c^2d2 are:

• -7c^2d2
• c^2d2

We can combine these terms by adding their coefficients:

-7c^2d2 + c^2d2 = -6c^2d2

Combining d^2 Terms

The term with the variable(s) d^2 is:

• 3d^2

This term does not have a like term to combine with, so it remains the same.

Combining cd^2 Terms

The term with the variable(s) cd^2 is:

• -4cd^2

This term does not have a like term to combine with, so it remains the same.

Combining c^2 Terms

The term with the variable(s) c^2 is:

• -c^2

This term does not have a like term to combine with, so it remains the same.

The Final Answer

After combining like terms, the final polynomial is:

${ 3c^2d - 6c^2d^2 + 3d^2 - 4cd^2 - c^2 }$

Conclusion

In this article, we have learned how to identify like terms and combine them to simplify a polynomial. By following the steps outlined in this article, we can rewrite a polynomial by combining like terms.