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

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

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Identify Row for Exponent 4: Identify the row of Pascal's Triangle that corresponds to the exponent 4. The row for the exponent 4 in Pascal's Triangle is the fifth row (starting with row 0 for the exponent 0), which has the coefficients 1, 4, 6, 4, 1.Write Binomial Expansion: Write out the terms using the binomial expansion theorem with the coefficients from Pascal's Triangle. The binomial expansion of (a+b)^4 is given by: 1*a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + 1*b^4 Substitute a with z^2 and b with 5x^2 to get: 1*(z^2)^4 + 4*(z^2)^3*(5x^2) + 6*(z^2)^2*(5x^2)^2 + 4*(z^2)*(5x^2)^3 + 1*(5x^2)^4Simplify Each Term: Simplify each term. Now we simplify each term: 1*(z^2)^4 = z^8 4*(z^2)^3*(5x^2) = 4*z^6*5x^2 = 20z^6x^2 6*(z^2)^2*(5x^2)^2 = 6*z^4*(5x^2)^2 = 6*z^4*25x^4 = 150z^4x^4 4*(z^2)*(5x^2)^3 = 4*z^2*(5x^2)^3 = 4*z^2*125x^6 = 500z^2x^6 1*(5x^2)^4 = (5x^2)^4 = 625x^8Combine Final Expanded Form: Combine all the terms to write the final expanded form. The final expanded form is: z^8 + 20z^6x^2 + 150z^4x^4 + 500z^2x^6 + 625x^8

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

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

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