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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 th Row: Identify the th row of Pascal's Triangle to determine the coefficients for the expansion of . The th row of Pascal's Triangle is .
- 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 terms of the form: , where ranges from to .
- Calculate Each Term: Calculate each term of the expansion using the coefficients and the powers of and . The terms are: $\(1\) \times (\(2\)y)^\(0\) \times x^\(5\) = x^\(5\)
- Combine Terms: Combine all the terms to write the expanded form of \((2y+x)^{5}\). The expanded form is: \(32y^{5} + 80y^{4}x + 80y^{3}x^{2} + 40y^{2}x^{3} + 10yx^{4} + x^{5}\)
