https://file.aiquickdraw.com/mathbot/file/1726116335648dy9vsijg.jpg

The problem asks to expand \((x - 4)^3\) and identify the coefficients of the terms in the expanded form.

We can use the binomial expansion formula to expand \((x - 4)^3\):

\[
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
\]

In this case, \(a = x\) and \(b = 4\), so:

\[
(x - 4)^3 = x^3 - 3x^2(4) + 3x(4^2) - 4^3
\]

Now, calculate each term:

1. \(x^3\) remains as \(x^3\).
2. \(-3x^2(4) = -12x^2\).
3. \(3x(4^2) = 3x(16) = 48x\).
4. \(-4^3 = -64\).

Thus, the expanded form is:

\[
x^3 - 12x^2 + 48x - 64
\]

From the expression in the image, the boxed values are:

- アイ = \(12\)
- ウエ = \(48\)
- オカ = \(64\)

Let me know if you'd like further clarification on this, or if you have other questions!

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Here are some related questions to consider:

1. How does the binomial expansion formula work for larger powers?
2. What is the general form for \((x - a)^n\)?
3. How do we expand expressions of the form \((ax + b)^n\)?
4. What other methods can we use to expand \((x - 4)^3\)?
5. How would the coefficients change if we expanded \((x + 4)^3\)?

**Tip**: Always check for patterns in binomial expansions—they can simplify complex terms into recognizable sequences!

次の式を展開せよ。 (x - 4)^3 = x^3 - アイ x^2 + ウエ x - オカ

This problem asks to expand the expression (x - 4)^3 using the binomial expansion formula. By applying the formula (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3, we can determine the coefficients for each term. Suitable for students in Grades 8-10, this exercise focuses on polynomial and binomial expansions.

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