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Answer :
Final answer:
The correct expansion of (1−3x)⁴ is 1 - 12x + 54x² - 108x³ + 81x⁴ using the binomial theorem. The provided options do not include this correct expansion.
Explanation:
When expanding the expression (1−3x)⁴, we need to use the binomial theorem, which allows us to expand expressions in the form of (a+b)⁴ as
- a⁴
- + 4a³b
- + 6a²b²
- + 4ab³
- + b⁴
In our case, a is 1 and b is -3x. Thus, we calculate each term as follows:
- 1⁴ = 1
- 4(1)³(-3x) = -12x
- 6(1)²(-3x)² = 6(9x²) = 54x²
- 4(1)(-3x)³ = -4(27x³) = -108x³
- (-3x)⁴ = 81x⁴
Combining these terms, we get the expanded expression: 1 - 12x + 54x² - 108x³ + 81x⁴. Therefore, the correct answer to the question is not explicitly listed in the multiple-choice options provided.
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