To rewrite the given expression a² + 2 - 72 in the form of (x + a)(x + b), we need to identify a and b values that would result in the same expression.
Here's how we can do it step by step:
1. First, let's compare the given expression a² + 2 - 72 with the form (x + a)(x + b).
2. We notice that a² corresponds to x² (since a is squared), and 2 corresponds to 2ab (since it is the product of the constants in the binomial form).
3. Therefore, in the given expression a² + 2 - 72, a would be the square root of the coefficient of a², which is a = √1 = 1.
4. Next, to find b, we take half of the coefficient of the linear term in the binomial form (2ab), which is 2. So, b = 2/2 = 1.
5. Now we substitute the values of a and b back into the form (x + a)(x + b). This gives us the expression as (x + 1)(x + 1), which simplifies to (x + 1)².
Therefore, the given expression a² + 2 - 72 can be rewritten as (x + 1)².
