To expand the expression $(3x - 1)(7x + 6)$, we use the distributive property (commonly called the FOIL method for binomials):

$(3x - 1)(7x + 6) = (3x \cdot 7x) + (3x \cdot 6) + (-1 \cdot 7x) + (-1 \cdot 6)$

Step-by-step:

1. $3x \cdot 7x = 21x^2$
2. $3x \cdot 6 = 18x$
3. $-1 \cdot 7x = -7x$
4. $-1 \cdot 6 = -6$

Now combine like terms:

$21x^2 + 18x - 7x - 6 = 21x^2 + 11x - 6$

Final Answer:

$21x^2 + 11x - 6$

Would you like a detailed explanation of any step?

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Here are 5 questions to deepen your understanding:

1. How does the distributive property work for more than two terms in each parenthesis?
2. What happens if one of the binomials has a negative sign outside?
3. How can we factor $21x^2 + 11x - 6$ back into its original binomials?
4. How do you verify that the expanded expression is correct?
5. Can you apply this method to $(2x + 3)(5x - 4)$?

Tip: Practice breaking down each term systematically to avoid errors in sign or coefficient calculation!