Bài 12.

`a)A = (x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)`

`= x(x^4 + 2x^3 + 4x^2 + 8x + 16) - 2(x^4 + 2x^3 + 4x^2 + 8x + 16)`

`= x^5 + 2x^4 + 4x^3 + 8x^2 + 16x - (2x^4 + 4x^3 + 8x^2 + 16x + 32)`

`= x^5 - 32`

Thay `x = 3` vào `A`, ta được:

`A = 3^5 - 32 = 243 - 32 = 211`

Vậy `A = 211` khi `x = 3`

`b)B = (x + 1)(x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)`

`= x(x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1) + 1(x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)`

`= x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1`

`= x^8 - 1`

Thay `x = 2` vào `B`, ta được:

`B = 2^8 - 1 = 256 - 1 = 255`

Vậy `B = 255` khi `x = 2`

`c)C = (x + 1)(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)`

`= x(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1) + 1(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)`

`= x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1`

`= x^7 + 1`

Thay `x = 2` vào `C`, ta được:

`C = 2^7 + 1 = 128 + 1 = 129`

Vậy `C = 129` khi `x = 2`

`d)D = 2x(10x^2 - 5x - 2) - 5x(4x^2 - 2x - 1)`

`= 20x^3 - 10x^2 - 4x - (20x^3 - 10x^2 - 5x)`

`= 20x^3 - 10x^2 - 4x - 20x^3 + 10x^2 + 5x`

`= x`

Thay `x = -5` vào `D`, ta được `D = -5`

Vậy `D = -5` khi `x = -5`

`e)E = (x - y)(x^2 - xy) - x(x^2 + 2y^2)`

`= x(x^2 - xy) - y(x^2 - xy) - (x^3 + 2xy^2)`

`= x^3 - x^2y - x^2y + xy^2 - x^3 - 2xy^2`

`= -2x^2y - xy^2`

Thay `x = 2, y = -3` vào `E`, ta được:

`E = -2 * 2^2 * (-3) - 2 * (-3)^2`

`= -2 * 4 * (-3) - 2 * 9`

`= 24 - 18`

`= 6`

Vậy `E = 6` khi `x = 2, y = -3`

Bài 13.

`a)(x + 2)(x + 3) - (x - 2)(x + 5) = 6`

`x^2 + 3x + 2x + 6 - (x^2 + 5x - 2x - 10) = 6`

`x^2 + 5x + 6 - (x^2 + 3x - 10) = 6`

`x^2 + 5x + 6 - x^2 - 3x + 10 = 6`

`2x + 16 = 6`

`2x = 6 - 16`

`2x = -10`

`x = -5`

Vậy `x = -5`

`b)(3x + 2)(2x + 9) - (x + 2)(6x + 1) = (x - 1) - (x - 6)`

`6x^2 + 27x + 4x + 18 - (6x^2 + x + 12x + 2) = x - 1 - x + 6`

`6x^2 + 31x + 18 - (6x^2 + 13x + 2) = 5`

`6x^2 + 31x + 18 - 6x^2 - 13x - 2 = 5`

`18x + 16 = 5`

`18x = 5 - 16`

`18x = -11`

`x = -11/18`

Vậy `x = -11/18`

`c)3(2x - 1)(3x - 1) - (2x - 3)(9x - 1) = 0`

`3(6x^2 - 2x - 3x + 1) - (18x^2 - 2x - 27x + 3) = 0`

`3(6x^2 - 5x + 1) - (18x^2 - 29x + 3) = 0`

`18x^2 - 15x + 3 - 18x^2 + 29x - 3 = 0`

`14x = 0`

`x = 0`

Vậy `x = 0`