Question

(x+8)(x-4)-(x+3)(x-2)+27

Answer 1

Ответ:

3x+1

Объяснение:

$(x + 8)(x - 4) - (x + 3)(x - 2) + 27 = {x}^{2} - 4x + 8x - 32 - ( {x}^{2} - 2x + 3x - 6) + 27 = {x}^{2} - 4x + 8x + 32 - {x}^{2} + 2x - 3x + 6 + 27 = 3x + 1$

Answer 2

To simplify the expression $(x+8)(x-4)-(x+3)(x-2)+27$, you can use the distributive property to expand each term, then combine like terms. Here's how you can do it step by step:

1. Expand the first term $(x+8)(x-4)$:

   $(x+8)(x-4) = x(x-4) + 8(x-4) = x^2 - 4x + 8x - 32$

   Simplify this to: $x^2 + 4x - 32$

2. Expand the second term $(x+3)(x-2)$:

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

   Simplify this to: $x^2 + x - 6$

3. Now, you have the expression as:

   $(x^2 + 4x - 32) - (x^2 + x - 6) + 27$

4. Distribute the negative sign to both terms inside the parentheses:

   $x^2 + 4x - 32 - x^2 - x + 6 + 27$

5. Combine like terms:

   $x^2 - x^2 + 4x - x - 32 + 6 + 27$

6. Simplify further:

   $3x - 32 + 6 + 27$

7. Combine constants:

   $3x - 32 + 33$

8. Simplify:

   $3x + 1$

So, the simplified expression is $3x + 1$.