https://file.aiquickdraw.com/mathbot/file/1726037255819d32c0c17.jpg

The problem shown in the image is:

**For all values of \( x \), (3x + 4)(4x - 3) = ?**

Let's solve it step-by-step:

1. Apply the distributive property (also known as FOIL method for binomials):
   \[
   (3x + 4)(4x - 3) = 3x \cdot 4x + 3x \cdot (-3) + 4 \cdot 4x + 4 \cdot (-3)
   \]
2. Simplify each term:
   \[
   = 12x^2 - 9x + 16x - 12
   \]
3. Combine like terms:
   \[
   = 12x^2 + 7x - 12
   \]

The correct expression is:

\[
12x^2 + 7x - 12
\]

Thus, the correct answer is **option 3**: \( 12x^2 + 7x - 12 \).

Do you want more details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. How do you apply the distributive property to multiply polynomials?
2. What is the FOIL method, and when is it used?
3. How do you combine like terms in an algebraic expression?
4. What are the steps for simplifying binomial multiplication?
5. Can you generalize the result of multiplying two binomials in terms of \(a\) and \(b\)?

**Tip:** Always check for common terms when simplifying, and remember to handle positive and negative signs carefully!

For all values of x, (3x + 4)(4x - 3) = ?

Learn how to solve the binomial multiplication problem (3x + 4)(4x - 3) using the distributive property and FOIL method. This step-by-step solution simplifies to a quadratic expression. Suitable for students in Grades 7-10.

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