Certainly! Let's expand the given expression step by step.
We start with the expression [tex]\((y-2)^2\)[/tex].
1. First, write it out as a product of two binomials:
[tex]\[
(y-2)^2 = (y-2)(y-2)
\][/tex]
2. Next, we apply the distributive property (also known as the FOIL method for binomials), which stands for First, Outer, Inner, Last:
[tex]\[
(y-2)(y-2) = y \cdot y + y \cdot (-2) + (-2) \cdot y + (-2) \cdot (-2)
\][/tex]
3. Now, we simplify each multiplication:
[tex]\[
= y^2 + (-2y) + (-2y) + 4
\][/tex]
4. Combine like terms:
[tex]\[
y^2 - 2y - 2y + 4 = y^2 - 4y + 4
\][/tex]
So, the expanded form of [tex]\((y-2)^2\)[/tex] is:
[tex]\[
y^2 - 4y + 4
\][/tex]
Thus, [tex]\((y-2)^2\)[/tex] is equivalent to [tex]\(y^2 - 4y + 4\)[/tex].
