Final answer:
To find the fifth term of (x²+y²)¹³, we use the binomial theorem and the general term expression T(r+1) = nCr * aⁿ⁻¹ * b¹. The fifth term can be calculated by finding 13C4, raising x² to the ninth power, y² to the fourth, and then multiplying these together.
Step-by-step explanation:
To determine the fifth term of the expansion of (x²+y²)¹³, we can use the binomial theorem. The general term of a binomial expansion is given by:
T(r+1) = nCr * aⁿ⁻¹ * b¹ where 'n' is the power, 'r' is the term number (starting from 0), 'a' and 'b' are the terms of the binomial, and nCr is the binomial coefficient for the given values of n and r.
Thus, for the fifth term (r=4), we would calculate it as follows:
- Find the binomial coefficient: 13C4
- Take the first term (x²) to the power of (13-4)
- Raise the second term (y²) to the power of 4
- Multiply these together to find the fifth term of the expansion.