Question

(x2+1)(x-3)-(2x-5)(3x+2)=x(x-5)

Answer 1

Решение:

(x2+1)(x-3)-(2x-5)(3x+2)=x(x-5)

Answer 2

Let's simplify the given expression step by step:

1. Expand both sets of parentheses: (x^2 + 1)(x - 3) = x^3 - 3x^2 + x - 3 (2x - 5)(3x + 2) = 6x^2 + 4x - 15x - 10 = 6x^2 - 11x - 10

2. Now, we have: (x^2 + 1)(x - 3) - (2x - 5)(3x + 2) = (x^3 - 3x^2 + x - 3) - (6x^2 - 11x - 10)

3. Distribute the negative sign on the second set of parentheses: (x^3 - 3x^2 + x - 3) - (6x^2 - 11x - 10) = x^3 - 3x^2 + x - 3 - 6x^2 + 11x + 10

4. Combine like terms: x^3 - 3x^2 - 6x^2 + x + 11x - 3 + 10 = x^3 - 9x^2 + 12x + 7

So the simplified expression is: x^3 - 9x^2 + 12x + 7

Now, let's see if it is equal to the right-hand side expression x(x - 5):

x(x - 5) = x^2 - 5x

The expressions are not equal, as x^3 - 9x^2 + 12x + 7 is not equal to x^2 - 5x.

Hence, the given equation (x^2 + 1)(x - 3) - (2x - 5)(3x + 2) = x(x - 5) is not valid.