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

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Full solution

Q. Find the product. Simplify your answer.\newline(2g−2)(2g+2)(2g - 2)(2g + 2)
  1. Identify Form: Identify the form of the expression.\newlineWe have the expression (2g−2)(2g+2)(2g - 2)(2g + 2), which is in the form of (a−b)(a+b)(a - b)(a + b).\newlineSpecial case: (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2
  2. Identify Values: Identify the values of aa and bb. Compare (2g−2)(2g+2)(2g - 2)(2g + 2) with (a−b)(a+b)(a - b)(a + b). a=2ga = 2g b=2b = 2
  3. Apply Formula: Apply the difference of squares formula.\newlineUsing the formula (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2, we get:\newline(2g−2)(2g+2)=(2g)2−(2)2(2g - 2)(2g + 2) = (2g)^2 - (2)^2
  4. Calculate Squares: Calculate the squares of aa and bb.(2g)2−(2)2=(2g×2g)−(2×2)=4g2−4(2g)^2 - (2)^2 = (2g \times 2g) - (2 \times 2) = 4g^2 - 4

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