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

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Use Pascal's Triangle to expand  (3z-4)^(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 row for the exponent 4 in Pascal's Triangle is the fifth row (starting with row 0 for the exponent 0), which is 1, 4, 6, 4, 1.Write Expansion Terms: Write out the terms of the expansion using the coefficients from Pascal's Triangle. The expansion will have the form: (a+b)^4 = 1*a^4*b^0 + 4*a^3*b^1 + 6*a^2*b^2 + 4*a^1*b^3 + 1*a^0*b^4. In our case, a = 3z and b = -4.Substitute and Simplify: Substitute a = 3z and b = -4 into the expansion and simplify each term. The expansion becomes: 1*(3z)^4*(-4)^0 + 4*(3z)^3*(-4)^1 + 6*(3z)^2*(-4)^2 + 4*(3z)^1*(-4)^3 + 1*(3z)^0*(-4)^4.Calculate Each Term: Calculate each term separately. 1st term: 1*(3z)^4*(-4)^0 = 1*81z^4*1 = 81z^4 2nd term: 4*(3z)^3*(-4)^1 = 4*27z^3*(-4) = -432z^3 3rd term: 6*(3z)^2*(-4)^2 = 6*9z^2*16 = 864z^2 4th term: 4*(3z)^1*(-4)^3 = 4*3z*(-64) = -768z 5th term: 1*(3z)^0*(-4)^4 = 1*1*256 = 256Combine for Final Form: Combine all the terms to get the final expanded form. The expanded form is: 81z^4 - 432z^3 + 864z^2 - 768z + 256.

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

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