Question

(3x+1)(x-1)-(3x-1)(3x+1) спростить выражение

Answer 1

$(3x + 1)(x - 1) - (3x - 1)(3x + 1) = 3 {x}^{2} + x - 3x - 1 - (3 {x}^{2} - 1) = 3 {x}^{2} - 2x - 1 - 3 {x}^{2} + 1 = - 2x$

Answer 2

To simplify the given expression, let's expand both parts of it and then combine like terms:

Expression: (3x+1)(x-1) - (3x-1)(3x+1)

Step 1: Expand the first part (3x+1)(x-1) = 3x * x + 3x * (-1) + 1 * x + 1 * (-1) = 3x^2 - 3x + x - 1 = 3x^2 - 2x - 1

Step 2: Expand the second part (3x-1)(3x+1) = 3x * 3x + 3x * 1 - 1 * 3x - 1 * 1 = 9x^2 + 3x - 3x - 1 = 9x^2 - 1

Step 3: Combine the two parts (3x+1)(x-1) - (3x-1)(3x+1) = (3x^2 - 2x - 1) - (9x^2 - 1)

Step 4: Distribute the negative sign through the second part = 3x^2 - 2x - 1 - 9x^2 + 1

Step 5: Combine like terms = (3x^2 - 9x^2) - 2x + 1 - 1

Step 6: Simplify = -6x^2 - 2x

So the simplified expression is: -6x^2 - 2x