To simplify the expression \((21x - 1)(x + 30)\), you can use the distributive property (also known as FOIL in the case of binomials):

\[
(21x - 1)(x + 30)
\]

Expanding this step-by-step:

1. Multiply \(21x\) by \(x\):
   \[
   21x \cdot x = 21x^2
   \]
2. Multiply \(21x\) by \(30\):
   \[
   21x \cdot 30 = 630x
   \]
3. Multiply \(-1\) by \(x\):
   \[
   -1 \cdot x = -x
   \]
4. Multiply \(-1\) by \(30\):
   \[
   -1 \cdot 30 = -30
   \]

Now, combine all the terms:

\[
21x^2 + 630x - x - 30
\]

Simplify the like terms \(630x - x\):

\[
21x^2 + 629x - 30
\]

Thus, the simplified expression is:

\[
21x^2 + 629x - 30
\]

Would you like to explore this further or ask additional questions?

Here are some follow-up questions:
1. How do you factor quadratic expressions?
2. What are the properties of polynomials?
3. How does the distributive property work in other expressions?
4. How do you solve quadratic equations?
5. What are the uses of polynomials in real-world applications?

**Tip:** Always group like terms after expanding an expression to simplify the result easily.

Learn how to simplify the expression (21x - 1)(x + 30) step-by-step using the distributive property. This problem involves algebraic manipulation of polynomials and is suitable for students in Grades 7-9.

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