(8x-16-x^2) Factored. I tried using different number combinations, but nothing is coming out right!
To factor the expression (8x - 16 - x^2), we can follow these steps:
Step 1: Rearrange the expression. It is helpful to start with the terms in descending order of exponents:
x^2 - 8x + 16.
Step 2: Identify two numbers whose product is equal to the constant term (16) and whose sum is equal to the coefficient of the middle term (-8).
In this case, the product of the two numbers should be 16, and their sum should be -8. The two numbers that satisfy these conditions are -4 and -4.
Step 3: Rewrite the middle term (-8x) using the two numbers obtained in Step 2:
x^2 - 4x - 4x + 16.
Step 4: Group the terms and factor by grouping:
(x^2 - 4x) - (4x - 16).
Step 5: Factor out the greatest common factor from each group:
x(x - 4) - 4(x - 4).
Step 6: Notice that we now have a common binomial factor, (x - 4). Factor out this common factor:
(x - 4)(x - 4).
Step 7: Simplify further by using the exponent rule:
(x - 4)^2.
So, the factored form of (8x - 16 - x^2) is (x - 4)^2.