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Find the product. Simplify your answer. (2m−4)(2m+4)(2m-4)(2m+4)

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer. (2m−4)(2m+4)(2m-4)(2m+4)
  1. Identify special case: Identify the special case for the product (2m−4)(2m+4)(2m-4)(2m+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 (2m–4)(2m+4)(2m–4)(2m+4) with (a−b)(a+b)(a - b)(a + b). a=2ma = 2m b=4b = 4
  3. Apply difference of squares: Apply the difference of squares to expand (2m–4)(2m+4)(2m–4)(2m+4).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(2m–4)(2m+4)=(2m)2−(4)2(2m–4)(2m+4) = (2m)^2 - (4)^2
  4. Simplify expression: Simplify (2m)2−(4)2.(2m)^2 - (4)^2.(2m)2−(4)2(2m)^2 - (4)^2=(2m×2m)−(4×4)= (2m \times 2m) - (4 \times 4)=4m2−16= 4m^2 - 16

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