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

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Full solution

Q. Find the product. Simplify your answer.\newline(3m+2)(3m−2)(3m + 2)(3m - 2)
  1. Recognize pattern: Recognize the pattern in the expression (3m+2)(3m−2)(3m + 2)(3m - 2). This expression is in the form of (a+b)(a−b)(a + b)(a - b), which is a difference of squares. Special 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 (3m+2)(3m−2)(3m + 2)(3m - 2) with (a+b)(a−b)(a + b)(a - b). a=3ma = 3m b=2b = 2
  3. Apply difference of squares formula: Apply the difference of squares formula to expand (3m+2)(3m−2)(3m + 2)(3m - 2).\newline(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2\newline(3m+2)(3m−2)=(3m)2−(2)2(3m + 2)(3m - 2) = (3m)^2 - (2)^2
  4. Simplify expression: Simplify (3m)2−(2)2.(3m)^2 - (2)^2.(3m)2−(2)2=(3m×3m)−(2×2)(3m)^2 - (2)^2 = (3m \times 3m) - (2 \times 2)=9m2−4= 9m^2 - 4

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