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

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(3w−4)(3w+4)(3w - 4)(3w + 4)
  1. Identify Special Case: Identify the special case for the product (3w−4)(3w+4)(3w - 4)(3w + 4). This product 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 (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 Difference of Squares Formula: Apply the difference of squares formula to expand (3w−4)(3w+4)(3w - 4)(3w + 4).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(3w−4)(3w+4)=(3w)2−(4)2(3w - 4)(3w + 4) = (3w)^2 - (4)^2
  4. Simplify Expression: Simplify (3w)2−(4)2.(3w)^2 - (4)^2.(3w)2−(4)2(3w)^2 - (4)^2=(3w×3w)−(4×4)= (3w \times 3w) - (4 \times 4)=9w2−16= 9w^2 - 16

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