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 x^2 + 16x + 64. We need to factor this quadratic expression. Step 1: 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, x^2 corresponds to a^2, so a = x. The constant term 64 corresponds to b^2, so b = sqrt(64) = 8. Step 2: Check the middle term. The middle term of a perfect square trinomial should be 2ab. Using a=x and b=8, we calculate 2ab = 2(x)(8) = 16x. This matches the middle term of the given expression, 16x. Step 3: Factor the expression. Since it fits the perfect square trinomial form, we can write it as (a+b)^2. Substituting a=x and b=8: x^2 + 16x + 64 = (x + 8)^2 The completely factored form of the expression is: (x + 8)^2 What's next?