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.

Learn how to expand and simplify the binomial expression (x-7)(x+3) step by step using the distributive property. This problem focuses on algebraic concepts and helps in mastering binomial expansions. Suitable for students in Grades 8-10.

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