Question

-(b-2)(3-4b) (b+2)(3-2b) (b-4)^2

Answer 1

-(b-2)(3-4b)=-(3b-4b²-6+8b)=-3b+4b²+6-8b=4b²-11b+6

(b+2)(3-2b)=3b-4b²+6-4b=-4b²-b+6

(b-4)²=b²-8b+16

Answer 2

To simplify the given expression, let's expand each of the terms and then combine like terms, if any.

1. Expanding the first term: -(b-2)(3-4b) = -1 * (b * 3 + b * (-4) - 2 * 3 - 2 * (-4b)) = -1 * (3b - 4b^2 - 6 + 8b) = -3b + 4b^2 + 6 - 8b

2. Expanding the second term: (b+2)(3-2b) = b * 3 + b * (-2b) + 2 * 3 + 2 * (-2b) = 3b - 2b^2 + 6 - 4b

3. Expanding the third term: (b-4)^2 = (b-4) * (b-4) = b^2 - 4b - 4b + 16 = b^2 - 8b + 16

Now, let's put all the expanded terms together:

-(b-2)(3-4b) + (b+2)(3-2b) + (b-4)^2

= (-3b + 4b^2 + 6 - 8b) + (3b - 2b^2 + 6 - 4b) + (b^2 - 8b + 16)

Now, combine like terms:

= -3b + 4b^2 + 6 - 8b + 3b - 2b^2 + 6 - 4b + b^2 - 8b + 16

Group the terms:

= (4b^2 - 2b^2) + (-3b - 8b - 4b - 8b) + (6 + 6 + 16)

Combine like terms again:

= 2b^2 - 23b + 28

So, the simplified expression is 2b^2 - 23b + 28.