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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 row for the exponent is the fifth row (starting with row for the exponent ), which is .
- Write Expansion: Write out each term of the expansion using the coefficients from Pascal's Triangle.The expansion will have terms that correspond to , , , , and , multiplied by the coefficients , , , , respectively.
- Expand Binomial: Expand each term of the binomial using the binomial theorem.The terms will be:
- Simplify Terms: Simplify each term.Now we simplify each term by calculating the powers and multiplying by the coefficients:
- Combine and Write: Combine like terms and write the final expression.The final expanded form is:
