To solve the expression [tex]\(2y^2 - 4y\)[/tex], let's carefully break it down step by step.
1. Identify the terms:
- The expression [tex]\(2y^2 - 4y\)[/tex] consists of two terms:
- The first term is [tex]\(2y^2\)[/tex], which means 2 times [tex]\(y\)[/tex] squared.
- The second term is [tex]\(-4y\)[/tex], which means 4 times [tex]\(y\)[/tex] but negative.
2. Combine like terms (if any):
- In this case, there are no like terms to combine, as [tex]\(2y^2\)[/tex] and [tex]\(-4y\)[/tex] are different: one is proportional to [tex]\(y^2\)[/tex] (a quadratic term), and the other is proportional to [tex]\(y\)[/tex] (a linear term).
3. Factor the expression (if possible):
- We can factor out a common factor from both terms.
- The greatest common factor (GCF) of [tex]\(2y^2\)[/tex] and [tex]\(-4y\)[/tex] is [tex]\(2y\)[/tex].
4. Factor out the GCF:
- When you factor out [tex]\(2y\)[/tex], the expression looks as follows:
[tex]\[
2y(y - 2)
\][/tex]
- Here, [tex]\(2y\)[/tex] is taken outside, and inside the parentheses, we have the remaining factors from each initial term:
- From [tex]\(2y^2\)[/tex], we factor out [tex]\(2y\)[/tex] and are left with [tex]\(y\)[/tex].
- From [tex]\(-4y\)[/tex], we factor out [tex]\(2y\)[/tex] and are left with [tex]\(-2\)[/tex].
Thus, the fully factored form of the expression [tex]\(2y^2 - 4y\)[/tex] is:
[tex]\[
2y(y - 2)
\][/tex]
However, if the intention is to leave the expression in its simplified polynomial form without factoring, our final answer remains:
[tex]\[
2y^2 - 4y
\][/tex]
