Sure! Let's solve the problem step-by-step:
We are given the expression [tex]\((5s + 2)^2\)[/tex] and are asked to find its expanded form.
1. Start by writing out the expression:
[tex]\[
(5s + 2)^2
\][/tex]
2. Use the binomial expansion formula:
The binomial expansion for [tex]\((a + b)^2\)[/tex] is given by:
[tex]\[
(a + b)^2 = a^2 + 2ab + b^2
\][/tex]
3. Identify the terms [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
In our expression, [tex]\(a = 5s\)[/tex] and [tex]\(b = 2\)[/tex].
4. Apply the binomial expansion:
[tex]\[
(5s + 2)^2 = (5s)^2 + 2 \cdot (5s) \cdot 2 + 2^2
\][/tex]
5. Calculate each term individually:
- [tex]\((5s)^2 = 25s^2\)[/tex]
- [tex]\(2 \cdot (5s) \cdot 2 = 20s\)[/tex]
- [tex]\(2^2 = 4\)[/tex]
6. Combine these terms to write the expanded form:
[tex]\[
25s^2 + 20s + 4
\][/tex]
Hence, the expanded form of [tex]\((5s + 2)^2\)[/tex] is:
[tex]\[
25s^2 + 20s + 4
\][/tex]
