Math Problem Statement
次の式を展開せよ。 (x - 4)^3 = x^3 - アイ x^2 + ウエ x - オカ
Solution
The problem asks to expand and identify the coefficients of the terms in the expanded form.
We can use the binomial expansion formula to expand :
In this case, and , so:
Now, calculate each term:
- remains as .
- .
- .
- .
Thus, the expanded form is:
From the expression in the image, the boxed values are:
- アイ =
- ウエ =
- オカ =
Let me know if you'd like further clarification on this, or if you have other questions!
Here are some related questions to consider:
- How does the binomial expansion formula work for larger powers?
- What is the general form for ?
- How do we expand expressions of the form ?
- What other methods can we use to expand ?
- How would the coefficients change if we expanded ?
Tip: Always check for patterns in binomial expansions—they can simplify complex terms into recognizable sequences!
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Math Problem Analysis
Mathematical Concepts
Binomial Expansion
Cubic Equations
Polynomial Expansion
Formulas
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
Theorems
Binomial Theorem
Suitable Grade Level
Grades 8-10