Simplify. (2x+2)^(4)-(x+1)^(4)

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Expand Expression: We need to expand both expressions (2x+2)^(4) and (x+1)^(4) using the binomial theorem or by multiplying the binomials step by step.Expand (2x+2)^(4): First, let's expand (2x+2)^(4). This is equivalent to ((2(x+1))^4), which can be simplified by taking the 2^4 outside the binomial expansion. (2x+2)^(4) = (2^4) * (x+1)^(4)Factor Out Common Term: Now, we have (2^4) * (x+1)^(4) - (x+1)^(4). Since (x+1)^(4) is common in both terms, we can factor it out. (2^4) * (x+1)^(4) - (x+1)^(4) = ((2^4) - 1) * (x+1)^(4)Calculate Result: Calculate 2^4 and subtract 1 from it. (2^4) - 1 = 16 - 1 = 15Expand (x+1)^(4): Now, we have 15 * (x+1)^(4). We need to expand (x+1)^(4) using the binomial theorem or by multiplying the binomial by itself four times.Apply Binomial Theorem: Expanding (x+1)^(4) using the binomial theorem gives us: (x+1)^(4) = x^4 + 4x^3 + 6x^2 + 4x + 1Multiply by 15: Now, multiply the expanded form of (x+1)^(4) by 15: 15 * (x^4 + 4x^3 + 6x^2 + 4x + 1) = 15x^4 + 60x^3 + 90x^2 + 60x + 15Final Answer: The final answer is the expanded form of the expression: 15x^4 + 60x^3 + 90x^2 + 60x + 15

Simplify. $\newline$ $(2 x+2)^{4}-(x+1)^{4}$

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Simplify.\newline(2x+2)4−(x+1)4 (2 x+2)^{4}-(x+1)^{4} (2x+2)4−(x+1)4

Simplify. $\newline$ $(2 x+2)^{4}-(x+1)^{4}$