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
The expression given is 9 - 6p + p^2. We need to factor this quadratic expression. Step 1: Rearrange the terms in descending order of the variable p. p^2 - 6p + 9 Step 2: Identify if the expression is a perfect square trinomial. A perfect square trinomial has the form a^2 - 2ab + b^2 = (a-b)^2. In our expression, p^2 corresponds to a^2, so a = p. The constant term 9 corresponds to b^2, so b = sqrt(9) = 3. Step 3: Check the middle term. The middle term of a perfect square trinomial should be -2ab. Using a=p and b=3, we calculate -2ab = -2(p)(3) = -6p. This matches the middle term of the given expression, -6p. Step 4: Factor the expression. Since it fits the perfect square trinomial form, we can write it as (a-b)^2. Substituting a=p and b=3: p^2 - 6p + 9 = (p - 3)^2 The completely factored form of the expression is: (p - 3)^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.