Factorization of Algebraic Expression: 2x^3+2xy^3+4x^2y^2-2xy
In this article, we will explore the factorization of the algebraic expression 2x^3+2xy^3+4x^2y^2-2xy. Factorization is an essential concept in algebra, where we express an algebraic expression as a product of simpler expressions.
Step 1: Identify the Greatest Common Factor (GCF)
The first step in factorizing the expression is to identify the Greatest Common Factor (GCF) of all the terms. By observing the expression, we can see that the GCF is 2xy.
Factorization
Now, we can rewrite the expression as:
2x^3 + 2xy^3 + 4x^2y^2 - 2xy = 2xy(x^2 + y^3 + 2xy - 1)
Simplification
We can further simplify the expression by combining like terms:
= 2xy(x^2 + y^3 + 2xy - 1) = 2xy(x^2 + y^3 + 2xy - 1) = 2xy(x + y)(x - y)(x + y^2)
Therefore, the factorized form of the expression 2x^3+2xy^3+4x^2y^2-2xy is 2xy(x + y)(x - y)(x + y^2).
Conclusion
In this article, we have successfully factorized the algebraic expression 2x^3+2xy^3+4x^2y^2-2xy. The factorized form of the expression is 2xy(x + y)(x - y)(x + y^2). This process is essential in algebra and has numerous applications in mathematics and other fields.
