To simplify the expression $(x+7)(x-3)$, we'll use the distributive property (also known as the FOIL method for binomials):

$(x+7)(x-3) = x(x-3) + 7(x-3)$

Now, distribute each term:

$= x^2 - 3x + 7x - 21$

Combine the like terms:

$= x^2 + 4x - 21$

So, the simplified expression is:

$x^2 + 4x - 21$

Would you like further details or have any questions? Here are some related questions:

1. What is the factorization of $x^2 + 4x - 21$?
2. How do you solve quadratic equations like $x^2 + 4x - 21 = 0$?
3. What is the graph of the quadratic equation $y = x^2 + 4x - 21$?
4. How do you use the quadratic formula to solve $x^2 + 4x - 21 = 0$?
5. Can you factor $x^2 + 4x - 21$ using other methods?

Tip: When expanding binomials, always remember to multiply each term in the first binomial by each term in the second binomial (distribute).