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

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

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Identify Exponent Row: Identify the row of Pascal's Triangle that corresponds to the exponent 4. The 5th row (since we start counting from the 0th row for the exponent 0) of Pascal's Triangle is 1, 4, 6, 4, 1. These numbers will be the coefficients in our expanded expression.Write Binomial Theorem: Write out the terms of the expansion using the binomial theorem. 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 (x^2 - z^2)^4, a = x^2, b = z^2, and n = 4. We will use the coefficients from Pascal's Triangle to expand the expression.Apply Coefficients: Apply the coefficients to each term of the expansion. The expanded form will be: 1*(x^2)^4*(z^2)^0 + 4*(x^2)^3*(z^2)^1 + 6*(x^2)^2*(z^2)^2 + 4*(x^2)^1*(z^2)^3 + 1*(x^2)^0*(z^2)^4Simplify Terms: Simplify each term of the expansion. Now we simplify the powers of x^2 and z^2 in each term: 1*x^8*z^0 + 4*x^6*z^2 + 6*x^4*z^4 + 4*x^2*z^6 + 1*z^8 Since z^0 = 1, we can simplify further: x^8 + 4*x^6*z^2 + 6*x^4*z^4 + 4*x^2*z^6 + z^8Final Simplified Expression: Write the final expanded expression in simplest form. The final expanded expression in simplest form is: x^8 + 4x^6z^2 + 6x^4z^4 + 4x^2z^6 + z^8

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

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