How would you simplify the expression 10k^3 + 2k^2 - 5k^3?

How would you simplify the expression 10k^3 + 2k^2 - 5k^3?

• A. 5k^3 + 2k^2
• B. 7k^3 + 2k^2
• C. 2k^2
• D. 5k^3 - 2k^2

Answer: (A)

To simplify the expression 10k^3 + 2k^2 - 5k^3, it's important to identify and combine like terms. The like terms in this expression are those that have the same variable raised to the same power. In this case, we have: - 10k^3 and -5k^3 as the like terms with the variable k raised to the power of 3. - 2k^2 is a separate like term, with k raised to the power of 2. Now, let's combine the like terms for k^3: 10k^3 - 5k^3 equals (10 - 5)k^3, which simplifies to 5k^3. Next, we retain the 2k^2 since there are no other k^2 terms to combine it with. Putting it all together, we have: 5k^3 + 2k^2. This result represents the correct simplification of the original expression. The answer aligns perfectly with choice A, 5k^3 + 2k^2, confirming its correctness as the combined form of the original terms.

To simplify the expression 10k^3 + 2k^2 - 5k^3, it's important to identify and combine like terms. The like terms in this expression are those that have the same variable raised to the same power. In this case, we have:

• 10k^3 and -5k^3 as the like terms with the variable k raised to the power of 3.

• 2k^2 is a separate like term, with k raised to the power of 2.

Now, let's combine the like terms for k^3:

10k^3 - 5k^3 equals (10 - 5)k^3, which simplifies to 5k^3.

Next, we retain the 2k^2 since there are no other k^2 terms to combine it with.

Putting it all together, we have:

5k^3 + 2k^2.

This result represents the correct simplification of the original expression. The answer aligns perfectly with choice A, 5k^3 + 2k^2, confirming its correctness as the combined form of the original terms.