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

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Full solution

Q. Find the product. Simplify your answer.\newline(2w−3)(2w+3)(2w - 3)(2w + 3)
  1. Recognize pattern: Recognize the pattern in the expression (2w−3)(2w+3)(2w - 3)(2w + 3). This is a difference of squares pattern, which can be written as (a−b)(a+b)(a - b)(a + b). Special 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 (2w−3)(2w+3)(2w - 3)(2w + 3) with (a−b)(a+b)(a - b)(a + b). a=2wa = 2w b=3b = 3
  3. Apply formula: Apply the difference of squares formula to expand (2w−3)(2w+3)(2w - 3)(2w + 3).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(2w−3)(2w+3)=(2w)2−(3)2(2w - 3)(2w + 3) = (2w)^2 - (3)^2
  4. Simplify: Simplify (2w)2−(3)2.(2w)^2 - (3)^2.(2w)2−(3)2=(2w×2w)−(3×3)(2w)^2 - (3)^2 = (2w \times 2w) - (3 \times 3)=4w2−9= 4w^2 - 9

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