To expand $(x-7)(x+3)$, we can use the distributive property (also known as FOIL for binomials):

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

Now distribute each term:

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

Now combine like terms:

$x^2 + 3x - 7x - 21 = x^2 - 4x - 21$

So, $(x-7)(x+3) = x^2 - 4x - 21$.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. Expand $(x-5)(x+8)$.
2. Expand $(x+6)(x-9)$.
3. Factor $x^2 - 3x - 10$.
4. Solve $(x+4)(x-2) = 0$.
5. Expand $(2x - 3)(x + 5)$.

Tip: When expanding binomials, always distribute both terms in the first binomial to both terms in the second.