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Find the product. Simplify your answer.\newline(k+1)(k−1)(k + 1)(k - 1)

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(k+1)(k−1)(k + 1)(k - 1)
  1. Identify special case: Identify the special case for the product (k+1)(k−1)(k + 1)(k - 1). 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 (k+1)(k−1)(k + 1)(k - 1) with (a+b)(a−b)(a + b)(a - b). a=ka = k b=1b = 1
  3. Apply difference of squares formula: Apply the difference of squares formula to expand (k+1)(k−1)(k + 1)(k - 1).\newline(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2\newline(k+1)(k−1)=k2−12(k + 1)(k - 1) = k^2 - 1^2
  4. Simplify expression: Simplify k2−12k^2 - 1^2. \newlinek2−12=k2−1k^2 - 1^2 = k^2 - 1

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