To solve the given problem, we need to expand the expression [tex]\((y + 5)^2\)[/tex].
Let's break this down step by step.
1. Understand the initial problem:
[tex]\((y + 5)^2\)[/tex]
This represents a binomial squared, which generally follows the formula:
[tex]\[(a + b)^2 = a^2 + 2ab + b^2\][/tex]
Here, [tex]\(a = y\)[/tex] and [tex]\(b = 5\)[/tex].
2. Apply the formula:
Using the formula for squaring a binomial, we substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[
(y + 5)^2 = y^2 + 2 \cdot y \cdot 5 + 5^2
\][/tex]
3. Perform the multiplications:
- [tex]\(y^2\)[/tex] remains [tex]\(y^2\)[/tex],
- [tex]\(2 \cdot y \cdot 5\)[/tex] equals [tex]\(10y\)[/tex],
- [tex]\(5^2\)[/tex] equals [tex]\(25\)[/tex].
4. Combine all the terms:
[tex]\[
(y + 5)^2 = y^2 + 10y + 25
\][/tex]
Thus, the expanded form of [tex]\((y + 5)^2\)[/tex] is:
[tex]\[
R = y^2 + 10y + 25
\][/tex]
