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Find the product. Simplify your answer.\newline(2v−2)(2v+2)(2v - 2)(2v + 2)

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Full solution

Q. Find the product. Simplify your answer.\newline(2v−2)(2v+2)(2v - 2)(2v + 2)
  1. Identify Form of Expression: Identify the form of the expression.\newlineThe expression (2v−2)(2v+2)(2v - 2)(2v + 2) is in the form of (a−b)(a+b)(a - b)(a + b), which is a difference of squares.\newlineSpecial case: (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2
  2. Identify Values of aa and bb: Identify the values of aa and bb. Compare (2v−2)(2v+2)(2v - 2)(2v + 2) with (a−b)(a+b)(a - b)(a + b). a=2va = 2v b=2b = 2
  3. Apply Difference of Squares Formula: Apply the difference of squares formula.\newlineUsing the values of aa and bb, we apply the formula (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2.\newline(2v−2)(2v+2)=(2v)2−(2)2(2v - 2)(2v + 2) = (2v)^2 - (2)^2
  4. Calculate Squares of a and b: Calculate the squares of a and b.\newline(2v)2−(2)2=(2v×2v)−(2×2)(2v)^2 - (2)^2 = (2v \times 2v) - (2 \times 2)\newline=4v2−4= 4v^2 - 4

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