Sure! Let's rewrite and simplify the expression [tex]\((u + 7)^2\)[/tex].
To expand [tex]\((u + 7)^2\)[/tex], we use the algebraic identity [tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex].
In this case, [tex]\(a = u\)[/tex] and [tex]\(b = 7\)[/tex]. Applying the identity:
1. [tex]\(a^2 = u^2\)[/tex]
2. [tex]\(2ab = 2 \cdot u \cdot 7 = 14u\)[/tex]
3. [tex]\(b^2 = 7^2 = 49\)[/tex]
Therefore, we can write:
[tex]\[
(u + 7)^2 = u^2 + 2 \cdot u \cdot 7 + 7^2
\][/tex]
By simplifying the terms:
[tex]\[
(u + 7)^2 = u^2 + 14u + 49
\][/tex]
So, the simplified expression for [tex]\((u + 7)^2\)[/tex] is:
[tex]\[
u^2 + 14u + 49
\][/tex]
