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

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(2f−2)(2f+2)(2f - 2)(2f + 2)
  1. Identify Problem Structure: Identify the structure of the problem.\newlineThe problem (2f−2)(2f+2)(2f - 2)(2f + 2) 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 of aa and bb: Identify the values of aa and bb. Compare (2f−2)(2f+2)(2f - 2)(2f + 2) with (a−b)(a+b)(a - b)(a + b). a=2fa = 2f b=2b = 2
  3. Apply Difference of Squares Formula: Apply the difference of squares formula to expand (2f−2)(2f+2)(2f - 2)(2f + 2).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(2f−2)(2f+2)=(2f)2−(2)2(2f - 2)(2f + 2) = (2f)^2 - (2)^2
  4. Simplify Expression: Simplify (2f)2−(2)2.(2f)^2 - (2)^2.(2f)2−(2)2=(2f×2f)−(2×2)(2f)^2 - (2)^2 = (2f \times 2f) - (2 \times 2)=4f2−4= 4f^2 - 4

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