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Find the product. Simplify your answer.\newline(3w+4)(3w−4)(3w + 4)(3w - 4)

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Full solution

Q. Find the product. Simplify your answer.\newline(3w+4)(3w−4)(3w + 4)(3w - 4)
  1. Identify Form: Identify the form of the expression.\newlineThe expression (3w+4)(3w−4)(3w + 4)(3w - 4) 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 (3w+4)(3w−4)(3w + 4)(3w - 4) with (a+b)(a−b)(a + b)(a - b). a=3wa = 3w b=4b = 4
  3. Apply Formula: Apply the difference of squares formula.\newlineUsing the formula (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2, we get:\newline(3w+4)(3w−4)=(3w)2−(4)2(3w + 4)(3w - 4) = (3w)^2 - (4)^2
  4. Calculate Squares: Calculate the squares of aa and bb.(3w)2=9w2(3w)^2 = 9w^2(4)2=16(4)^2 = 16
  5. Subtract Squares: Subtract the square of bb from the square of aa.9w2−169w^2 - 16

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