Question

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

Answer 1

Ответ:

(3x-2)2+(2x-1)(2x+1)-2(x-4)(x+3)=6x-4+$4x^{2}$-1-$2x^{2}$-6x+8x+24=$2x^{2}$+8x+19

Объяснение:

Answer 2

To simplify the expression:

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

Let's break it down step by step.

Step 1: Expand the square of the first term using the formula (a - b)^2 = a^2 - 2ab + b^2.

(3x - 2)^2 = (3x)^2 - 2(3x)(2) + 2^2 = 9x^2 - 12x + 4

Step 2: Expand the second term using the FOIL method.

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

Step 3: Expand the third term using the FOIL method.

-2(x - 4)(x + 3) = -2 * (x * x + x * 3 - 4 * x - 4 * 3) = -2 * (x^2 + 3x - 4x - 12) = -2 * (x^2 - x - 12) = -2x^2 + 2x + 24

Now, substitute the expanded forms back into the original expression:

(9x^2 - 12x + 4) + (4x^2 - 1) - (-2x^2 + 2x + 24)

Combining like terms:

9x^2 - 12x + 4 + 4x^2 - 1 + 2x^2 - 2x - 24

Combine the x^2 terms, x terms, and constant terms:

(9x^2 + 4x^2 + 2x^2) + (-12x - 2x) + (4 - 1 - 24)

15x^2 - 14x - 21

Therefore, the simplified expression is 15x^2 - 14x - 21.