This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given expression. The expression shown in the image is m^3 - 3m^2 + 3m - 1. Step 2: Recognize the algebraic identity. This expression matches the expansion of a binomial cubed, specifically (a-b)^3. The formula for (a-b)^3 is: (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 Step 3: Compare the given expression with the identity. By comparing m^3 - 3m^2 + 3m - 1 with a^3 - 3a^2b + 3ab^2 - b^3, we can see that a=m and b=1. Step 4: Substitute the values into the identity. Substituting a=m and b=1 into (a-b)^3: (m-1)^3 = m^3 - 3(m)^2(1) + 3(m)(1)^2 - (1)^3 (m-1)^3 = m^3 - 3m^2 + 3m - 1 Thus, the expression m^3 - 3m^2 + 3m - 1 can be factored as (m-1)^3. The simplified expression is: (m-1)^3 Send me the next one 📸