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

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(2w+3)(2w−3)(2w + 3)(2w - 3)
  1. Special Case Identification: Which special case applies here?\newline(2w+3)(2w−3)(2w + 3)(2w - 3) 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. Values of aa and bb: 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. Difference of Squares Application: Apply the difference of squares 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)2−32(2w + 3)(2w - 3) = (2w)^2 - 3^2
  4. Simplification: Simplify (2w)2−32.(2w)^2 - 3^2.(2w)2−32=(2w⋅2w)−(3⋅3)=4w2−9(2w)^2 - 3^2 = (2w \cdot 2w) - (3 \cdot 3) = 4w^2 - 9

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