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

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(2g−3)(2g+3)(2g - 3)(2g + 3)
  1. Identify Special Case: Identify the special case that applies here.\newline(2g−3)(2g+3)(2g - 3)(2g + 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. Identify Values of aa and bb: Identify the values of aa and bb. Compare (2g−3)(2g+3)(2g - 3)(2g + 3) with (a−b)(a+b)(a - b)(a + b). a=2ga = 2g b=3b = 3
  3. Apply Difference of Squares: Apply the difference of squares to expand (2g−3)(2g+3)(2g - 3)(2g + 3).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(2g−3)(2g+3)=(2g)2−32(2g - 3)(2g + 3) = (2g)^2 - 3^2
  4. Simplify Expression: Simplify (2g)2−32.(2g)^2 - 3^2.(2g)2−32=(2g⋅2g)−(3⋅3)(2g)^2 - 3^2 = (2g \cdot 2g) - (3 \cdot 3)=4g2−9= 4g^2 - 9

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