Final answer:
The expansion of (a + b)⁶ with a = 1 and b = 0.3 results in (1.3)⁶. Only option A is correct, resulting in 1.892 upon calculation. Other options incorrectly apply the binomial coefficients for different powers of 0.3.
Step-by-step explanation:
The complete expansion of (a + b)⁶ with a = 1 and b = 0.3 is found using the binomial theorem. The correct expansion would involve terms with increasing powers of 0.3 and decreasing powers of 1, each multiplied by their respective binomial coefficients. Here is the step by step explanation to calculate each term correctly:
- Σn=0⁶ (⁶Cn)(a⁶-n)(bⁱ)
- ⁶Cn is the binomial coefficient, calculated as 6!/(n!(6-n)!).
- For term A, the calculation is (1⁶)(0.3⁰), which results in 1.
- For term B, the calculation involves the binomial coefficient 6: 6(1⁵)(0.3ⁱ), which does not equal to 4.284.
- For term C, the coefficient is 15: 15(1⁴)(0.3), which is not 9.222.
- For term D, the coefficient is 20: 20(1³)(0.3³), and this is also incorrect.
Since we have been given a = 1 and b = 0.3, plugging these values into the binomial expansion formula gives us the expanded form of (1 + 0.3)⁶, which can be calculated correctly with a calculator. Using the given values for a and b, and knowing their sum 1.3 can be raised to the sixth power directly, we can disregard the rest of the binomial expansion for the simplification of the calculation under these conditions. The only correct calculation for (1 + 0.3)⁶ is thus option A, which equals 1.892 when evaluated and rounded.