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Find the product. Simplify your answer.\newline(3c−2)(3c+2)(3c - 2)(3c + 2)

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Full solution

Q. Find the product. Simplify your answer.\newline(3c−2)(3c+2)(3c - 2)(3c + 2)
  1. Identify Form: Identify the form of the expression.\newlineThe expression (3c−2)(3c+2)(3c - 2)(3c + 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: Identify the values of aa and bb. Compare (3c−2)(3c+2)(3c - 2)(3c + 2) with (a−b)(a+b)(a - b)(a + b). a=3ca = 3c b=2b = 2
  3. Apply 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(3c−2)(3c+2)=(3c)2−(2)2(3c - 2)(3c + 2) = (3c)^2 - (2)^2
  4. Simplify Expression: Simplify the expression.\newline(3c)2−(2)2(3c)^2 - (2)^2\newline= (3c×3c)−(2×2)(3c \times 3c) - (2 \times 2)\newline= 9c2−49c^2 - 4

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