Answer:
-(x - 4)^2
See below.
Step-by-step explanation:
Problem 1.
-x^2 + 8x - 16 =
First, factor -1 out of all terms. It can be written as simply a negative sign to the left of parentheses.
= -(x^2 - 8x + 16)
Now we factor the trinomial. We are told it is the square of a binomial.
x^2 is the square of x. 16 is the square of 4 and of -4. Since the middle term is negative, as in -8x, we need -4.
= -(x - 4)^2
Problem 2.
0.48xy + 36y^2 + 0.16x^2 =
First, rearrange the terms in order: x^2, xy, y^2.
= 0.16x^2 + 0.48xy + 36y^2
All terms are positive, so we only need the positive square roots.
The first term of the binomial is the square root of 0.16x^2, so it is 0.4x.
The second term of the binomial is the square root of 36y^2, so it is 6y.
= (0.4x + 6y)^2
As you pointed out, this gives 0.16x^2 + 4.8xy + 36x^2, which is not the original trinomial. The given trinomial is not the square of a binomial, and the problem is incorrect.
Factor 0.16x^2 + 0.48xy + 36y^2
0.16x^2 + 0.48xy + 36y^2 =
= 0.16(x^2 + 3xy + 225y^2)
For x^2 + 3xy + 225y^2 to factor as the square of a binomial, the middle term would have to be 2 * x * 15y = 30xy. The middle term is 1/10 of that, 3xy. This trinomial is not the square of a binomial.
