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Use Pascal's Triangle to expand . Express your answer in simplest form.Answer:
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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 fourth row of Pascal's Triangle because the rows are indexed starting from for the exponent . The fourth row of Pascal's Triangle is .
- Write Expansion Terms: Write out each term of the expansion using the coefficients from Pascal's Triangle.The expansion will have four terms, corresponding to the coefficients . Each term will be of the form . The powers of the first term decrease from to , and the powers of the second term increase from to .
- Calculate First Term: Calculate the first term of the expansion.Using the first coefficient from Pascal's Triangle, which is , the first term is .
- Calculate Second Term: Calculate the second term of the expansion.Using the second coefficient from Pascal's Triangle, which is , the second term is .
- Calculate Third Term: Calculate the third term of the expansion.Using the third coefficient from Pascal's Triangle, which is , the third term is .
- Calculate Fourth Term: Calculate the fourth term of the expansion.Using the fourth coefficient from Pascal's Triangle, which is , the fourth term is
- Combine Terms: Combine all the terms to write the final expanded form.The expanded form of is .
