Combine like terms: -4x^3 - 6y^3 + y^3 - 3 + x^3 + x^3 + 4y^3.

Question image

Understand the Problem

The question is asking to combine similar algebraic terms in the expression provided.

Answer

$$ -2x^3 - y^3 - 3 $$
Answer for screen readers

The combined expression is: $$ -2x^3 - y^3 - 3 $$

Steps to Solve

  1. Identify like terms

In the expression, find the terms with the same variable raised to the same power. Here, we have three types of terms: those containing $x^3$, those containing $y^3$, and the constant.

  1. Combine the $x^3$ terms

The $x^3$ terms in the expression are: $$ -4x^3 + x^3 + x^3 $$ First, add the coefficients: $$ -4 + 1 + 1 = -2 $$ So, the combined $x^3$ terms give us: $$ -2x^3 $$

  1. Combine the $y^3$ terms

Next, we look at the $y^3$ terms: $$ -6y^3 + y^3 + 4y^3 $$ Again, add the coefficients: $$ -6 + 1 + 4 = -1 $$ Thus, the combined $y^3$ terms result in: $$ -1y^3 $$

  1. Combine the constant term

The only constant term in the expression is $-3$. This remains as is since there are no other constants to combine it with.

  1. Write the final expression

Now that we have combined all the like terms, we can write the final result as: $$ -2x^3 - y^3 - 3 $$

The combined expression is: $$ -2x^3 - y^3 - 3 $$

More Information

Combining like terms is a fundamental skill in algebra, making expressions simpler and easier to work with. In this case, we grouped similar variable terms to form a more concise expression.

Tips

  • Ignoring constants: Often, students forget to include constant terms when combining or simplifying expressions.
  • Misadding coefficients: Adding coefficients incorrectly, especially with negative numbers, can lead to wrong results.
Thank you for voting!
Use Quizgecko on...
Browser
Browser