(x%5E4%2B3x%5E3-2x%5E3y%5E2x%5E4%2B3x%5E3-2x%5E3)%2By(x%5E4%2B3x%5E3-2x%5E3).jpeg "(y^2+y)(x^4+3x^3-2x^3y^2x^4+3x^3-2x^3)+y(x^4+3x^3-2x^3)")
Simplifying the Expression: (y^2+y)(x^4+3x^3-2x^3y^2x^4+3x^3-2x^3)+y(x^4+3x^3-2x^3)
This expression might look intimidating at first, but it can be simplified with careful observation and basic algebraic manipulation. Let's break it down step by step.
Identifying the Common Factor
First, notice that the term (x^4+3x^3-2x^3) appears in both parts of the expression. This is a common factor that can be factored out.
Factoring Out the Common Factor
Let's rewrite the expression factoring out the common term:
(y^2+y)(x^4+3x^3-2x^3) + y(x^4+3x^3-2x^3) = (x^4+3x^3-2x^3)(y^2+y+y)
Simplifying the Expression
Now we have a much simpler expression:
(x^4+3x^3-2x^3)(y^2+2y)
We can further simplify this by combining the like terms within the first set of parentheses:
(x^4+x^3)(y^2+2y)
Final Simplified Expression
The final simplified form of the given expression is (x^4+x^3)(y^2+2y).
Key Takeaways:
- Identify common factors: This is crucial for simplifying expressions.
- Factoring out: Using the distributive property in reverse can significantly reduce complexity.
- Combining like terms: Always simplify expressions by combining similar terms.