Faktorization of the Expression 15x^3y^4-20x^4y^3+30x^3y^3
In this article, we will explore the factorization of the algebraic expression 15x^3y^4-20x^4y^3+30x^3y^3.
Step 1: Find the Greatest Common Factor (GCF)
The first step in factorizing the expression is to find the greatest common factor (GCF) of all the terms. The GCF is the product of the common factors of all the terms.
In this case, the GCF is x^3y^3.
Expression with GCF factored out
15x^3y^4 - 20x^4y^3 + 30x^3y^3 = x^3y^3(15y - 20x + 30)
Step 2: Factorize the remaining expression
Now, we need to factorize the remaining expression inside the parentheses.
15y - 20x + 30 = 5(3y - 4x + 6)
Final factored form
Therefore, the final factored form of the expression 15x^3y^4 - 20x^4y^3 + 30x^3y^3 is:
15x^3y^4 - 20x^4y^3 + 30x^3y^3 = x^3y^3(5)(3y - 4x + 6)
By factorizing the expression, we can simplify it and make it easier to work with. Factorization is an important concept in algebra and is used in various mathematical operations, such as solving equations and simplifying expressions.
