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Factor the expression: m3 - 3m2 + 3m - 1

Mathematics

ScanSolve AI Answer

Answer

(m−1)3(m-1)^3

Step-by-step solution

4 steps
  1. Identify the given expression.

    The expression shown in the image is m3−3m2+3m−1m^3 - 3m^2 + 3m - 1.

  2. Recognize the algebraic identity.

    This expression matches the expansion of a binomial cubed, specifically (a−b)3(a-b)^3. The formula for (a−b)3(a-b)^3 is:

    (a−b)3=a3−3a2b+3ab2−b3(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
  3. Compare the given expression with the identity.

    By comparing m3−3m2+3m−1m^3 - 3m^2 + 3m - 1 with a3−3a2b+3ab2−b3a^3 - 3a^2b + 3ab^2 - b^3, we can see that a=ma=m and b=1b=1.

  4. Substitute the values into the identity.

    Substituting a=ma=m and b=1b=1 into (a−b)3(a-b)^3:

    (m−1)3=m3−3(m)2(1)+3(m)(1)2−(1)3(m-1)^3 = m^3 - 3(m)^2(1) + 3(m)(1)^2 - (1)^3 (m−1)3=m3−3m2+3m−1(m-1)^3 = m^3 - 3m^2 + 3m - 1

    Thus, the expression m3−3m2+3m−1m^3 - 3m^2 + 3m - 1 can be factored as (m−1)3(m-1)^3.

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