Use Pascal's Triangle to expand (4y^(2)+1)^(3). Express your answer in simplest form. Answer:

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Use Pascal's Triangle to expand  (4y^(2)+1)^(3). 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 of the binomial expansion. Since we are expanding (4y^(2)+1)^(3), we need the fourth row of Pascal's Triangle, which corresponds to the coefficients for a cubic expansion. The fourth row of Pascal's Triangle is 1, 3, 3, 1.Write Expansion Terms: Write out each term of the expansion using the binomial theorem and the coefficients from Pascal's Triangle. The binomial theorem states that (a+b)^n = Σ (n choose k) * a^(n-k) * b^k, where Σ denotes the sum over k from 0 to n. Using the coefficients from Pascal's Triangle, the expansion will be: 1*(4y^2)^3*(1)^0 + 3*(4y^2)^2*(1)^1 + 3*(4y^2)^1*(1)^2 + 1*(4y^2)^0*(1)^3Calculate Each Term: Calculate each term of the expansion. 1*(4y^2)^3*(1)^0 = 1*(64y^6)*(1) = 64y^6 3*(4y^2)^2*(1)^1 = 3*(16y^4)*(1) = 48y^4 3*(4y^2)^1*(1)^2 = 3*(4y^2)*(1) = 12y^2 1*(4y^2)^0*(1)^3 = 1*(1)*(1) = 1Combine Terms for Final Form: Combine all the terms to write the final expanded form. The expanded form of (4y^(2)+1)^(3) is: 64y^6 + 48y^4 + 12y^2 + 1

Use Pascal's Triangle to expand $\left(4 y^{2}+1\right)^{3}$ . Express your answer in simplest form. $\newline$ Answer:

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Use Pascal's Triangle to expand $\left(4 y^{2}+1\right)^{3}$ . Express your answer in simplest form. $\newline$ Answer: