Question

(x-3)(x-4)-(x-5)(x-2)

Answer 1

X²-4x-3x+12-x²+2x+5x-10=x(-4-3+2+5)+2=0+2=2

Answer 2

Let's simplify the given expression step by step:

1. Expand the terms within each set of parentheses: $(x - 3)(x - 4) = x^2 - 4x - 3x + 12 = x^2 - 7x + 12$ $(x - 5)(x - 2) = x^2 - 2x - 5x + 10 = x^2 - 7x + 10$

2. Substitute these expanded expressions back into the original expression: $(x - 3)(x - 4) - (x - 5)(x - 2) = (x^2 - 7x + 12) - (x^2 - 7x + 10)$

3. Distribute the negative sign to each term in the second set of parentheses: $x^2 - 7x + 12 - x^2 + 7x - 10$

4. Combine like terms: $- 7x + 12 + 7x - 10$

5. The $7x$ and $-7x$ terms cancel out: $12 - 10 = 2$

So, the simplified expression is $2$.