(3x%2By%5E2)-(6x%5E4y-2xy%5E4)-2xy.jpeg "(x^2-y)(3x+y^2)-(6x^4y-2xy^4) 2xy")
Simplifying the Expression (x^2-y)(3x+y^2)-(6x^4y-2xy^4) 2xy
This article will guide you through simplifying the algebraic expression: (x^2-y)(3x+y^2)-(6x^4y-2xy^4) 2xy.
Step 1: Expand the first product
Begin by expanding the product of the two binomials: (x^2-y)(3x+y^2)
Using the FOIL method (First, Outer, Inner, Last), we get:
- First: x^2 * 3x = 3x^3
- Outer: x^2 * y^2 = x^2y^2
- Inner: -y * 3x = -3xy
- Last: -y * y^2 = -y^3
Combining these terms, we have: (x^2-y)(3x+y^2) = 3x^3 + x^2y^2 - 3xy - y^3
Step 2: Distribute the second product
Next, we distribute the 2xy term to the expression within the parentheses:
(6x^4y - 2xy^4) 2xy = 12x^5y^2 - 4x^2y^5
Step 3: Combine the expanded terms
Now, we combine the expanded terms from steps 1 and 2:
3x^3 + x^2y^2 - 3xy - y^3 - (12x^5y^2 - 4x^2y^5)
Distributing the negative sign, we get:
3x^3 + x^2y^2 - 3xy - y^3 - 12x^5y^2 + 4x^2y^5
Step 4: Rearrange the terms
Rearrange the terms in descending order of their exponents:
-12x^5y^2 + 4x^2y^5 + 3x^3 + x^2y^2 - 3xy - y^3
Final Result
Therefore, the simplified form of the given expression is:
-12x^5y^2 + 4x^2y^5 + 3x^3 + x^2y^2 - 3xy - y^3