Use Pascal's Triangle to expand (x^(2)+2z)^(4). Express your answer in simplest form. Answer:

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Use Pascal's Triangle to expand  (x^(2)+2z)^(4). Express your answer in simplest form. Answer:

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Identify Row: Identify the row of Pascal's Triangle that corresponds to the exponent 4. The fourth row (starting with row 0) of Pascal's Triangle is 1, 4, 6, 4, 1.Write Expansion Terms: Write out the terms of the expansion using the coefficients from Pascal's Triangle. The expansion will have terms that correspond to the coefficients 1, 4, 6, 4, 1. Each term will be of the form (x^(2))^(4-k) * (2z)^(k), where k is the term number starting from 0.Calculate Each Term: Calculate each term of the expansion. The terms are: 1st term: (x^(2))^(4-0) * (2z)^(0) = x^(8) * 1 = x^(8) 2nd term: 4 * (x^(2))^(4-1) * (2z)^(1) = 4 * x^(6) * 2z = 8x^(6)z 3rd term: 6 * (x^(2))^(4-2) * (2z)^(2) = 6 * x^(4) * (2z)^(2) = 6 * x^(4) * 4z^(2) = 24x^(4)z^(2) 4th term: 4 * (x^(2))^(4-3) * (2z)^(3) = 4 * x^(2) * (2z)^(3) = 4 * x^(2) * 8z^(3) = 32x^(2)z^(3) 5th term: (x^(2))^(4-4) * (2z)^(4) = 1 * (2z)^(4) = 16z^(4)Combine Terms: Combine all the terms to write the expanded form of the polynomial. The expanded form is: x^(8) + 8x^(6)z + 24x^(4)z^(2) + 32x^(2)z^(3) + 16z^(4)

Use Pascal's Triangle to expand $\left(x^{2}+2 z\right)^{4}$ . Express your answer in simplest form. $\newline$ Answer:

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Use Pascal's Triangle to expand (x2+2z)4 \left(x^{2}+2 z\right)^{4} (x2+2z)4. Express your answer in simplest form.\newlineAnswer:

Use Pascal's Triangle to expand $\left(x^{2}+2 z\right)^{4}$ . Express your answer in simplest form. $\newline$ Answer: