You provided the expression \((3x + 2)(7x - 4)\). Let's expand it using the distributive property (also known as the FOIL method for binomials):

\[
(3x + 2)(7x - 4)
\]

### Step-by-Step Expansion:

1. Multiply the first terms: \(3x \times 7x = 21x^2\).
2. Multiply the outer terms: \(3x \times -4 = -12x\).
3. Multiply the inner terms: \(2 \times 7x = 14x\).
4. Multiply the last terms: \(2 \times -4 = -8\).

Now, combine the results:

\[
21x^2 - 12x + 14x - 8
\]

Combine like terms \((-12x + 14x)\):

\[
21x^2 + 2x - 8
\]

So, the expanded form of the expression is:

\[
21x^2 + 2x - 8
\]

Would you like further details or have any questions about this?

Here are 5 related questions to practice:
1. Expand \((4x + 5)(6x - 3)\).
2. Factor \(12x^2 + 5x - 2\).
3. Solve for \(x\) in the equation \((2x + 3)(x - 1) = 0\).
4. Simplify the expression \((x + 4)(x - 5)\).
5. Expand \((2x - 3)(5x + 7)\).

**Tip:** Always combine like terms carefully when expanding or simplifying expressions!

Expand the binomial expression (3x + 2)(7x - 4) using the distributive property. This step-by-step solution simplifies the expression to 21x^2 + 2x - 8. Learn key algebraic concepts such as binomial expansion and combining like terms. Suitable for students in Grades 8-10.

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