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Find the square. Simplify your answer.\newline(a−1)2(a - 1)^2

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the square. Simplify your answer.\newline(a−1)2(a - 1)^2
  1. Identify Formula: Identify the expression to be squared and the special case formula to use.\newlineThe expression given is (a−1)2(a - 1)^2, which is in the form of (a−b)2(a - b)^2.\newlineSpecial case: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
  2. Identify Values: Identify the values of aa and bb in the expression.\newlineIn the expression (a−1)2(a - 1)^2, we compare it to (a−b)2(a - b)^2 to find:\newlinea=aa = a\newlineb=1b = 1
  3. Apply Formula: Apply the square of a binomial formula to expand (a−1)2(a - 1)^2.\newlineUsing the formula (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2, we get:\newline(a−1)2=a2−2(a)(1)+12(a - 1)^2 = a^2 - 2(a)(1) + 1^2
  4. Simplify Expression: Simplify the expanded expression.\newlinea2−2(a)(1)+12a^2 - 2(a)(1) + 1^2\newline= a2−2a+1a^2 - 2a + 1

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