y 3 −y 2 +4y 3 +7y 2−3x 3+y 2 +4y 3 combine the like terms

To combine like terms in the expression:

\[
y^3 - y^2 + 4y^3 + 7y^2 - 3x^3 + y^2 + 4y^3
\]

Let's first group the like terms:

- \( y^3 \)-terms: \( y^3 + 4y^3 + 4y^3 \)
- \( y^2 \)-terms: \( -y^2 + 7y^2 + y^2 \)
- \( x^3 \)-term: \( -3x^3 \)

Now, let's simplify each group:

- \( y^3 \)-terms: \( y^3 + 4y^3 + 4y^3 = 9y^3 \)
- \( y^2 \)-terms: \( -y^2 + 7y^2 + y^2 = 7y^2 \)
- \( x^3 \)-term: \( -3x^3 \)

So, the simplified expression is:

\[
9y^3 + 7y^2 - 3x^3
\]

Would you like further explanation or details?

Here are 5 related questions to explore:

1. How do you factor expressions like \( 9y^3 + 7y^2 - 3x^3 \)?
2. What are like terms in algebraic expressions?
3. How do you identify terms to combine in a polynomial?
4. How do coefficients affect combining like terms?
5. What are the differences between \( x^3 \) and \( y^3 \) in an algebraic context?

**Tip**: Always make sure to look for the same powers of variables when combining like terms in polynomials!

y^3 − y^2 + 4y^3 + 7y^2 − 3x^3 + y^2 + 4y^3 combine the like terms

Learn how to combine like terms in the polynomial expression y^3 − y^2 + 4y^3 + 7y^2 − 3x^3 + y^2 + 4y^3. This problem explains the algebraic process of grouping and simplifying similar terms with the same variable powers. Suitable for students in Grades 7-9.

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