The expression \((7x + 1)\) squared can be expanded using the formula for a binomial square:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \(a = 7x\) and \(b = 1\), so:

\[
(7x + 1)^2 = (7x)^2 + 2(7x)(1) + (1)^2
\]

Now, simplifying each term:

\[
(7x)^2 = 49x^2
\]
\[
2(7x)(1) = 14x
\]
\[
(1)^2 = 1
\]

Thus, the expanded form of \((7x + 1)^2\) is:

\[
49x^2 + 14x + 1
\]

Would you like more details on the binomial expansion or any other clarification?

### Related Questions:
1. How would you expand \((3x - 5)^2\)?
2. What is the formula for the expansion of \((a + b)^3\)?
3. Can you expand and simplify \((4x + 2)(4x - 2)\)?
4. How do you factor the expression \(49x^2 + 14x + 1\)?
5. How can you apply the quadratic formula to solve \(49x^2 + 14x + 1 = 0\)?

### Tip:
When squaring binomials, remember to account for the middle term, which comes from \(2ab\).

Understand how to expand and simplify the expression (7x + 1)^2 using the binomial expansion formula. This detailed solution covers key algebraic concepts, including binomial expansion, polynomials, and how to apply the formula (a + b)^2 = a^2 + 2ab + b^2. Suitable for students in Grades 8-10.

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