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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 . The th row (since we start counting from the th row for the exponent ) of Pascal's Triangle is . These numbers will be the coefficients in the expanded form.
- Write Expansion Terms: Write out the terms 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 .For , the expanded form will be:
- Simplify Each Term: Simplify each term of the expansion.Now we will simplify each term by calculating the powers and multiplying the coefficients:
- Combine Coefficients: Combine the coefficients and simplify the terms.Now we multiply the coefficients together for each term:
- Write Final Form: Write the final expanded form in simplest terms.The final expanded form of is:
