To expand the expression $(7x + 3)^2$, we use the formula for the square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

Here, $a = 7x$ and $b = 3$. Applying the formula, we get:

$(7x + 3)^2 = (7x)^2 + 2 \cdot (7x) \cdot 3 + 3^2$

Now, calculate each term:

1. $(7x)^2 = 49x^2$
2. $2 \cdot (7x) \cdot 3 = 42x$
3. $3^2 = 9$

Putting it all together, we have:

$(7x + 3)^2 = 49x^2 + 42x + 9$

Would you like more details or have any questions? Here are some more questions you might be interested in:

1. How do you expand $(x + 5)^2$?
2. What is the derivative of $49x^2 + 42x + 9$?
3. How do you solve the quadratic equation $49x^2 + 42x + 9 = 0$?
4. What are the roots of $49x^2 + 42x + 9 = 0$?
5. How do you factor the expression $49x^2 + 42x + 9$?

Tip: Always double-check your work by substituting back into the original equation to ensure it holds true.