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

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Use Pascal's Triangle to expand  (3z^(2)+5x^(2))^(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 of Pascal's Triangle (since we start counting from the 0th row) is 1, 4, 6, 4, 1.Write Coefficients: Write out each term of the expansion using the coefficients from Pascal's Triangle. The expansion will have 5 terms, corresponding to the coefficients 1, 4, 6, 4, 1.Apply Binomial Expansion: Apply the binomial expansion using the coefficients and the variables (3z^(2)) and (5x^(2)). The terms will be: 1*(3z^(2))^4*(5x^(2))^0 +  4*(3z^(2))^3*(5x^(2))^1 +  6*(3z^(2))^2*(5x^(2))^2 +  4*(3z^(2))^1*(5x^(2))^3 +  1*(3z^(2))^0*(5x^(2))^4Calculate Each Term: Calculate each term separately. 1st term: 1*(3z^(2))^4*(5x^(2))^0 = 1*(81z^(8))*(1) = 81z^(8) 2nd term: 4*(3z^(2))^3*(5x^(2))^1 = 4*(27z^(6))*(5x^(2)) = 540z^(6)x^(2) 3rd term: 6*(3z^(2))^2*(5x^(2))^2 = 6*(9z^(4))*(25x^(4)) = 1350z^(4)x^(4) 4th term: 4*(3z^(2))^1*(5x^(2))^3 = 4*(3z^(2))*(125x^(6)) = 1500z^(2)x^(6) 5th term: 1*(3z^(2))^0*(5x^(2))^4 = 1*(1)*(625x^(8)) = 625x^(8)Combine Final Form: Combine all the terms to get the final expanded form. The expanded form is: 81z^(8) + 540z^(6)x^(2) + 1350z^(4)x^(4) + 1500z^(2)x^(6) + 625x^(8)

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

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Use Pascal's Triangle to expand (3z2+5x2)4 \left(3 z^{2}+5 x^{2}\right)^{4} (3z2+5x2)4. Express your answer in simplest form.\newlineAnswer:

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