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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 Exponent Row: Identify the row of Pascal's Triangle that corresponds to the exponent . The third row of Pascal's Triangle (starting with row ) is . These numbers will be the coefficients in the expansion.
- Write Expansion Terms: Write out the terms of the expansion using the binomial theorem and the coefficients from Pascal's Triangle.The expansion will have four terms, with the coefficients , , , and , respectively. The first term will have , the second term will have multiplied by , the third term will have multiplied by , and the fourth term will have .
- Calculate Each Term: Calculate each term of the expansion.First term: Second term: Third term: Fourth term:
- Combine Terms: Combine all the terms to write the expanded form.The expanded form is .
