Question

(x-3)^2 - (x-1)(x-4)+(x-2)(x+2)

Answer 1

Х^2+12x-9-x^2-x-x+4+x^2-4=12x-9-2x=10x-9

Answer 2

To simplify the expression (x-3)^2 - (x-1)(x-4) + (x-2)(x+2), we can start by expanding the squared term:

(x-3)^2 = (x-3)(x-3) = x^2 - 3x - 3x + 9 = x^2 - 6x + 9

Next, we can expand the other two terms using the distributive property:

-(x-1)(x-4) = -(x^2 - 4x - x + 4) = -x^2 + 5x - 4

(x-2)(x+2) = x^2 + 2x - 2x - 4 = x^2 - 4

Now we can substitute these results back into the original expression:

(x-3)^2 - (x-1)(x-4) + (x-2)(x+2) = (x^2 - 6x + 9) - (-x^2 + 5x - 4) + (x^2 - 4)

Simplifying further, we combine like terms:

x^2 - 6x + 9 + x^2 - 5x + 4 + x^2 - 4

Now, we can combine the x^2 terms, the x terms, and the constant terms:

x^2 + x^2 + x^2 - 6x - 5x + 9 + 4 - 4

Finally, we simplify:

3x^2 - 11x + 9

Therefore, the simplified form of the expression (x-3)^2 - (x-1)(x-4) + (x-2)(x+2) is 3x^2 - 11x + 9.