(x-7)%2B1.jpeg "(x-9)(x-7)+1")
Expanding and Simplifying (x-9)(x-7)+1
This expression involves expanding a product of binomials and then simplifying the result. Here's how to break it down:
1. Expanding the Binomial Product
We can use the FOIL method (First, Outer, Inner, Last) to expand the product of the binomials:
(x-9)(x-7) = x * x + x * (-7) + (-9) * x + (-9) * (-7)
Simplifying this:
(x-9)(x-7) = x² - 7x - 9x + 63
2. Combining Like Terms
Next, combine the -7x and -9x terms:
(x-9)(x-7) = x² - 16x + 63
3. Adding the Constant
Finally, add the constant term +1 to the expression:
(x-9)(x-7) + 1 = x² - 16x + 63 + 1
4. Final Simplified Expression
The simplified expression is:
(x-9)(x-7) + 1 = x² - 16x + 64
This is a quadratic expression in standard form. You can further manipulate it, for example, by factoring it into (x-8)(x-8) or by finding its roots.