simplify each exression 7x^2 - 4x^2 y -x^2 + 8x^2 y

Let's simplify the given expression step by step:

The expression is:

\[
7x^2 - 4x^2y - x^2 + 8x^2y
\]

1. Combine the like terms involving \( x^2 \):
   \[
   7x^2 - x^2 = (7 - 1)x^2 = 6x^2
   \]

2. Now combine the terms involving \( x^2y \):
   \[
   -4x^2y + 8x^2y = (8 - 4)x^2y = 4x^2y
   \]

3. Finally, combine the results:
   \[
   6x^2 + 4x^2y
   \]

So, the simplified expression is:

\[
6x^2 + 4x^2y
\]

Would you like a detailed breakdown or have any questions?

Here are 5 related questions to explore further:
1. How would you factorize the expression \( 6x^2 + 4x^2y \)?
2. How can you identify like terms in algebraic expressions?
3. What is the difference between a monomial and a binomial?
4. How can expressions with multiple variables, like \( x^2y \), be simplified further?
5. Can you apply this method to simplify \( 9x^2 - 5x^2y + 3x^2y - 2x^2 \)?

**Tip:** Always look for like terms (same variables raised to the same power) when simplifying algebraic expressions.

simplify each expression 7x^2 - 4x^2 y -x^2 + 8x^2 y

Learn how to simplify the expression 7x^2 - 4x^2y - x^2 + 8x^2y with step-by-step guidance. This problem covers algebraic concepts such as combining like terms and simplification. Ideal for students in Grades 7-9.

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