`1)` `x^2 - 8x` `+ 16 - y^2`

`= (x - 4)^2 - y^2`

`= (x` `- 4 - y``) (x -` `4 + y)`

`2)` `4x^2 - y^2` `+ 10y - 25`

`= 4x^2` `- (y^2 -` `10y + 25)`

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

`= (2x` `- y + 5``) (2x +` `y - 5)`

`(864 × 48 - 432 × 96)/(864 × 48 + 432)`

`= (432 × 2 × 48 - 432 × 96)/(432 × 2 × 48 + 432 × 1)`

`= (432 × (2 × 48 - 96))/(432 × (2 × 48 + 1))`

`= (432 × 0)/(432 × 97)`

`= 0`

`A = x^2` `- 4x + 7`

   `= x^2 - 4x` `+ 4 + 3`

   `= (x - 2)^2 + 3` `≥ 3 ∀ x`

Dấu `"="` xảy ra `<=>` `x - 2 =` `0 <=>` `x = 2`

Vậy `Amin =` `3 <=>` `x = 2`

`C =` `x^2 + 8x`

    `= x^2 + 8x` `+ 16 - 16`

    `= (x + 4)^2 - 16` `≥ -16 ∀ x`

Dấu `"="` xảy ra `<=>` `x + 4 =` `0 <=>` `x = -4`

Vậy `Bmin =` `-16 <=>` `x = -4`

`C = -2x^2` `+ 8x - 15`

   `= -2``(x^2 -` `4x + 15/2)`

   `= -2(``x^2 - 4x +` `4 + 7/2)`

   `=` `-2(x - 2)^2 - 7` `≥ -7 ∀ x`

Dấu `"="` xảy ra `<=> x` `- 2 = 0` `<=>` `x = 2`

Vậy `Cmin = -7` `<=>` `x = 2`

`a)` `2x (x -` `7) + 5x` `- 35 = 0`

`=>` `2x (x` `- 7) +` `5(x -` `7) = 0`

`=> (``2x + 5``) (x -` `7) = 0`

`=>` $\left[\begin{matrix} 2x + 5 = 0\\ x - 7 = 0\end{matrix}\right.$

`=>` $\left[\begin{matrix} 2x = -5\\ x = 7\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{-5}{2}\\ x = 7\end{matrix}\right.$

`b)` `x (x -` `3) - 7x` `+ 21 = 0`

`=>` `x(x` `- 3) -` `7(x -` `3) = 0`

`=> (``x - 7``) (x -` `3) = 0`

`=>` $\left[\begin{matrix} x - 7 = 0\\ x - 3 = 0\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = 7\\ x = 3\end{matrix}\right.$

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

`= (``x - y)` `(x + y``) + 3(``x - y)`

`= (``x - y``) (x +` `y + 3)`

`a,` Ta có `: AB =` `OB - OA`

         `=>` `AB =` `7 - 3`

         `=>` `AB = 4cm`

`b,` Vì `M` là trung điểm của `OA`

Mà `OA = 3cm`

`=> OM` `= MA =` `3/2 = 1,5cm`

Vì `N` là trung điểm của `OB`

Mà `OB = 7cm`

`=> ON` `= NB =` `7/2 = 3,5cm`

Ta có : AN = AB - NB

        => AN = 4 - 3,5

        => AN = 0,5cm

Lại có `: MA +` `AN = MN`

        `=>` `1,5 +` `0,5 = MN`

        `=>` `2 = MN`

        `=>` `MN = 2cm`

`c,` Có `5` tia `:` `OM, OA``, ON,` `OB, Ox`

Mình gửi lại bài ạ

`a,` `-1/6x^3y^2z . (-2/3xy)^3`

`=` `-1/6x^3y^2z . (-8)/27x^3y^3`

`= (``-1/6 . (-8)/27``) . (``x^3 . x^3``) . (``y^2 . y^3``) . z`

`= 4/81x^6y^5z`

`b,` `(-2xy^2) .` `(3xyz)^2 . 2/5xyz`

`= -2xy^2 .` `9x^2y^2z^2 . 2/5xyz`

`= (-2` `. 9 .` `2/5) .` `(x .` `x^2 . x``) . (``y^2 . y^2` `. y)` `. (z^2` `. z)`

`= -36/5x^4y^5z^3`

`c,` `-3xz^2 . 1/3y^2z`

`= (``-3 .` `1/3) .` `x . y^2` `. (z^2` `. z)`

`= -xy^2z^3`

`d,` `2x^3y . [-3x(-y)]^2`

`=` `2x^3y . 9x^2y^2`

`= (2` `. 9)` `. (x^3` `. x^2)` `. (y` `. y^2)`

`= 18x^5y^3`

`e,` `1/2yz^2 . (-5/4x^2y^2z)`

`= (1/2` `. (-5)/4``) .` `x^2 . (``y . y^2``) . (z^2` `. z)`

`= -5/8x^2y^3z^3`

`f,` `(-2xy)^3 . xz^3`

`=` `-8x^3y^3 . xz^3`

`= -8 .` `(x^3 .` `x) .` `y^3 . z^3`

`= -8x^4y^3z^3`

`g, xy^2` `. (4x^2z^3) .` `1/2x . (-2/5x)^2`

`= xy^2` `. 4x^2z^3 .` `1/2x . 4/25x^2`

`= (``4 .` `1/2 . 4/25``) . (``x . x^2` `. x .` `x^2) .` `y^2 . z^3`

`= 1/50x^6y^2z^3`

`a,` Ta có `: AB =` `OB - OA`

         `=>` `AB =` `7 - 3`

         `=>` `AB = 4cm`

`b,` Vì `M` là trung điểm của `OA`

Mà `OA = 3cm`

`=> OM` `= MA =` `3/2 = 1,5cm`

Vì `N` là trung điểm của `OB`

Mà `OB = 7cm`

`=> ON` `= NB =` `7/2 = 3,5cm`

Ta có `: MA +` `AN = MN`

        `=>` `1,5 +` `3,5 = MN`

        `=>` `5 = MN`

        `=>` `MN = 5cm`

`c,` Có `5` tia `:` `OM, OA``, ON,` `OB, Ox`