Use Pascal's Triangle to expand (3z^(2)-4)^(3). Express your answer in simplest form. Answer:

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Use Pascal's Triangle to expand  (3z^(2)-4)^(3). 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 of the binomial expansion. Since we are expanding (3z^(2)-4)^(3), we need the fourth row of Pascal's Triangle (since the rows are indexed starting from 0). The fourth row of Pascal's Triangle is 1, 3, 3, 1.Write Expansion Terms: Write out each term of the expansion using the coefficients from Pascal's Triangle. The expansion will have four terms, corresponding to the coefficients 1, 3, 3, 1. Each term will be of the form (coefficient) * (first term in the binomial raised to a power) * (second term in the binomial raised to a power). The powers on the first term will decrease from 3 to 0, and the powers on the second term will increase from 0 to 3.Calculate First Term: Calculate the first term of the expansion. Using the first coefficient from Pascal's Triangle, which is 1, the first term is (1) * (3z^(2))^3 * (-4)^0. This simplifies to (1) * (27z^(6)) * (1), which is just 27z^(6).Calculate Second Term: Calculate the second term of the expansion. Using the second coefficient from Pascal's Triangle, which is 3, the second term is (3) * (3z^(2))^2 * (-4)^1. This simplifies to (3) * (9z^(4)) * (-4), which is -108z^(4).Calculate Third Term: Calculate the third term of the expansion. Using the third coefficient from Pascal's Triangle, which is 3, the third term is (3) * (3z^(2))^1 * (-4)^2. This simplifies to (3) * (3z^(2)) * (16), which is 144z^(2).Calculate Fourth Term: Calculate the fourth term of the expansion. Using the fourth coefficient from Pascal's Triangle, which is 1, the fourth term is (1) * (3z^(2))^0 * (-4)^3. This simplifies to (1) * (1) * (-64), which is -64.Combine Terms: Combine all the terms to write the final expanded form. The expanded form of (3z^(2)-4)^(3) is 27z^(6) - 108z^(4) + 144z^(2) - 64.

Use Pascal's Triangle to expand $\left(3 z^{2}-4\right)^{3}$ . Express your answer in simplest form. $\newline$ Answer:

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