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

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Full solution

Q. Find the product. Simplify your answer.\newline(t+1)(t−1)(t + 1)(t - 1)
  1. Perform Multiplication: Now we perform the actual multiplication for each pair of terms.\newlinet⋅t=t2t\cdot t = t^2 (First terms)\newlinet⋅(−1)=−tt\cdot(-1) = -t (Outer terms)\newline1⋅t=t1\cdot t = t (Inner terms)\newline1⋅(−1)=−11\cdot(-1) = -1 (Last terms)\newlineSo, (t+1)(t−1)=t2−t+t−1(t + 1)(t - 1) = t^2 - t + t - 1
  2. Combine Like Terms: Next, we combine like terms. The terms −t-t and tt cancel each other out because they are additive inverses.t2−t+t−1=t2−1t^2 - t + t - 1 = t^2 - 1
  3. Simplify Expression: We have now simplified the expression completely. The product of (t+1)(t−1)(t + 1)(t - 1) is t2−1t^2 - 1.

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