Factor 2x^2y-4xy+6xy^2
The given question is asking for the factoring of the polynomial expression "2x^2y - 4xy + 6xy^2". Factoring in mathematics refers to the process of breaking down an expression into products of simpler expressions, which when multiplied together give back the original expression. In this case, the goal would be to find common factors among the terms and rewrite the polynomial as a product of binomials, trinomials, or other factored expressions that when expanded will result in the original expression.
$2 x^{2} y - 4 x y + 6 x y^{2}$
Answer
Solution:
Step 1 Extract the common factor $2xy$ from the term $2x^2y$. This results in $2xy(x) - 4xy + 6xy^2$.
Step 2 Remove the common factor $2xy$ from the term $-4xy$. The expression now becomes $2xy(x) + 2xy(-2) + 6xy^2$.
Step 3 Take out the common factor $2xy$ from the term $6xy^2$. The equation simplifies to $2xy(x) + 2xy(-2) + 2xy(3y)$.
Step 4 Combine the terms with the common factor $2xy$. This gives us $2xy(x - 2) + 2xy(3y)$.
Step 5 Finally, factor out $2xy$ from the entire expression to get $2xy(x - 2 + 3y)$.
Knowledge Notes:
Factoring is the process of finding an equivalent expression that is a product of simpler or smaller expressions. In the context of algebra, factoring polynomials involves expressing the polynomial as a product of its factors, which may include numbers, variables, or other polynomials.
The steps involved in the problem-solving process for factoring the given polynomial $2x^2y - 4xy + 6xy^2$ are as follows:
Identify the common factor across all terms: In this case, each term of the polynomial has a common factor of $2xy$.
Factor out the common factor: This involves dividing each term by the common factor and writing the polynomial as the product of the common factor and the resulting simplified terms.
Simplify the expression: After factoring out the common factor, the terms inside the parentheses are simplified to their lowest terms.
Combine like terms: If there are like terms within the parentheses after factoring, they should be combined to simplify the expression further.
Write the final factored form: The polynomial is now expressed as the product of the common factor and the simplified expression within the parentheses.
In the given problem, the final factored form is $2xy(x - 2 + 3y)$, which is the product of the common factor $2xy$ and the binomial $x - 2 + 3y$.
