\(50^2-49^2+48^2-47^2+46^2-45^2+...+4^2-3^2+2^2\)

\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+\left(46-45\right)\left(46+45\right)...+\left(4-3\right)\left(4+3\right)+4\)

\(=99+95+91+...+7+3+1\)

\(=\left(3+99\right).\left[\left(99-3\right):4+1\right]:2+1\)

\(=102x25:2+1=1276\)

\(2n^2+5n-1=2n^2-n+6n-3+2\)

                            \(=n\left(2n-1\right)+3\left(2n-1\right)+2\)

Để \(2n^2+5n-1⋮2n-1\)thì \(2⋮2n-1\)

\(\Rightarrow2n-1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

Mà 2n - 1 là số lẻ nên:

\(2n-1\in\left\{-1;1\right\}\Rightarrow n\in\left\{0;1\right\}\)

Chúc bạn học tốt.

\(2n^2+5n-1\)chia hết cho \(2n-1\)

\(\Leftrightarrow2\)chia hết cho \(2n-1\)

\(\Leftrightarrow2n-1\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\)

\(\Leftrightarrow2n\in\left\{-1;0;2;3\right\}\)

\(\Leftrightarrow n\in\left\{-\frac{1}{2};0;1;\frac{3}{2}\right\}\)

Mà \(n\in Z\)

\(\Rightarrow n\in\left\{0;1\right\}\)

e)  \(\left(x-y\right)^2+4\left(x-y\right)-12\)

\(=\left(x-y\right)\left[\left(x-y\right)+4\right]-12\)

\(=\left(x-y\right)\left(x-y+4\right)-12\)

f)  \(x^2-2xy+y^2+3x-3y-10\)

\(=\left(x^2-2xy+y^2\right)+\left(3x-3y\right)-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

\(=\left(x-y\right)\left[\left(x-y\right)+3\right]-10\)

\(=\left(x-y\right)\left(x-y+3\right)-10\)

g)   \(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\)

\(=\left(x^2+4x+8\right)\left[\left(x^2+4x+8\right)+3x\right]+2x^2\)

\(=\left(x^2+4x+8\right)\left(x^2+4x+8+3x\right)+2x^2\)

\(=\left(x^2+4x+8\right)\left(x^2+7x+8\right)+2x^2\)

a ) K hóa trị I

b) NO₃ hóa trị I   ( Ba hóa trị II )

c) Fe hóa trị II

d) N hóa trị I

e) N hóa trị IV

f) ....

g) Al hóa trị III ( Al₂(SO₄)₃

a, Gọi hóa trị của K trong \(K_2SO_4\)là  x 

Theo qui tắc hóa trị, ta có:

        \(x.2=1.II\)

   \(\Rightarrow x=I\)

Vậy K trong K₂SO₄ có hóa trị I

Tương tự với các ý còn lại.

b, Bạn viết sai rồi Ba hóa trị 2 mà.

c, Fe (I)

d, N (I)

e, N (IV)

f, làm gì có NO²

g, Bạn viết sai CTHH rồi.

6. We really her sense of humor.

7. He ought not to play computer games.

8. Hilary doesn't have to wear uniform at school.

IV.  Viết lại câu với từ gợi ý .

6. We/ really / her/ sense/ humor.
................We really  her sense of humor.......................................................................................................
7. He ought/ not/ play computer games.
...................He ought not to play computer games................................................................................................
8. Hilary/ not/ have to/ wear/ uniform / at school.
..................Hilary does not have to wear uniform at school.................................................................

\(\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)

\(=\left(x^2+x\right)^2+2.\left(x^2+x\right).2+4-16\)

\(=\left(x^2+x+2\right)^2-4^2\)

\(=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)\)

\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)

       \(P=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)

Đặt \(x^2+x=t\) Khi đó:

\(P=t^2+4t-12\)

   \(=t^2+6t-2t-12\)

   \(=t\left(t+6\right)-2\left(t+6\right)\)

   \(=\left(t+6\right)\left(t-2\right)\)

   \(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)

   \(=\left(x^2+x+6\right)\left[x\left(x+2\right)-\left(x+2\right)\right]\)

   \(=\left(x^2+x+6\right)\left(x+2\right)\left(x-1\right)\)

       \(x^4+3x^2-4\)

\(=x^4+4x^2-x^2-4\)

\(=x^2\left(x^2+4\right)-\left(x^2+4\right)\)

\(=\left(x^2+4\right)\left(x^2-1\right)\)

\(=\left(x^2+4\right)\left(x-1\right)\left(x+1\right)\)

Chúc bạn học tốt.

IV.  Viết lại câu với từ gợi ý .

6. We/ really / her/ sense/ humor.
.......................We really  her sense of humor............................................................................................
7. He ought/ not/ play computer games.
..........He ought not to play computer games......................................................................................
8. Hilary/ not/ have to/ wear/ uniform / at school.
..........Hilary does not have to wear uniform at school...................................................................