Use Pascal's Triangle to expand (3z^(2)+5)^(4). Express your answer in simplest form. Answer:

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Use Pascal's Triangle to expand  (3z^(2)+5)^(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 5th row (since we start counting from 0) of Pascal's Triangle is 1, 4, 6, 4, 1. These numbers will be the coefficients in our expanded expression.Write Expansion Terms: Write out the terms of the expansion using the binomial theorem and the coefficients from Pascal's Triangle. The binomial theorem tells us that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where Σ denotes the sum over k from 0 to n. For (3z^(2) + 5)^4, we have: 1*(3z^(2))^4*(5)^0 + 4*(3z^(2))^3*(5)^1 + 6*(3z^(2))^2*(5)^2 + 4*(3z^(2))^1*(5)^3 + 1*(3z^(2))^0*(5)^4Calculate Each Term: Calculate each term of the expansion. 1*(3z^(2))^4*(5)^0 = 1*(81z^(8))*(1) = 81z^(8) 4*(3z^(2))^3*(5)^1 = 4*(27z^(6))*(5) = 540z^(6) 6*(3z^(2))^2*(5)^2 = 6*(9z^(4))*(25) = 1350z^(4) 4*(3z^(2))^1*(5)^3 = 4*(3z^(2))*(125) = 1500z^(2) 1*(3z^(2))^0*(5)^4 = 1*(1)*(625) = 625Combine for Final Form: Combine all the terms to write the final expanded form. The expanded form of (3z^(2) + 5)^4 is: 81z^(8) + 540z^(6) + 1350z^(4) + 1500z^(2) + 625

Use Pascal's Triangle to expand $\left(3 z^{2}+5\right)^{4}$ . Express your answer in simplest form. $\newline$ Answer:

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Use Pascal's Triangle to expand (3z2+5)4 \left(3 z^{2}+5\right)^{4} (3z2+5)4. Express your answer in simplest form.\newlineAnswer:

Use Pascal's Triangle to expand $\left(3 z^{2}+5\right)^{4}$ . Express your answer in simplest form. $\newline$ Answer: