To expand the expression \((6 - x)(4 + 3x)\), we'll apply the distributive property (also known as the FOIL method for binomials):

\[
(6 - x)(4 + 3x) = 6 \cdot 4 + 6 \cdot 3x - x \cdot 4 - x \cdot 3x
\]

Calculating each term individually:

1. \(6 \cdot 4 = 24\)
2. \(6 \cdot 3x = 18x\)
3. \(-x \cdot 4 = -4x\)
4. \(-x \cdot 3x = -3x^2\)

Now, combining these results:

\[
24 + 18x - 4x - 3x^2
\]

Then, combining like terms (\(18x - 4x\)):

\[
= -3x^2 + 14x + 24
\]

Thus, the expanded form of \((6 - x)(4 + 3x)\) is:

\[
-3x^2 + 14x + 24
\]

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

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1. How would you expand \((x + 2)(x - 5)\)?
2. What happens when both binomials are identical, like \((3x - 1)^2\)?
3. How can you apply the distributive property to expand \((x - 6)(x + 7)\)?
4. What if the expression were \((6 - x)(4 - 3x)\) instead?
5. How do you factor \(-3x^2 + 14x + 24\) back into its original form?

**Tip:** Always combine like terms carefully in polynomial expansion to ensure accuracy.

Learn how to expand the expression (6 - x)(4 + 3x) step-by-step using the distributive property. This problem guides you through polynomial expansion, focusing on combining like terms for an accurate result, suitable for students in Grades 7-9.

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