AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Use Pascal's Triangle to expand . Express your answer in simplest form.Answer:
Full solution
Q. Use Pascal's Triangle to expand . Express your answer in simplest form.Answer:
- Identify Row: Identify the row of Pascal's Triangle that corresponds to the exponent of the binomial expansion.Since we are expanding , we need the row of Pascal's Triangle, which corresponds to the coefficients for a cubic expansion.The row of Pascal's Triangle is .
- Write Expansion Terms: Write out each term of the expansion using the binomial theorem and the coefficients from Pascal's Triangle.The binomial theorem states that , where denotes the sum over from to .Using the coefficients from Pascal's Triangle, the expansion will be:
- Calculate Each Term: Calculate each term of the expansion.
- Combine Terms for Final Form: Combine all the terms to write the final expanded form.The expanded form of is:
