Bài 1:

a) \(3x^2-9x=3x\left(x-3\right)\)

b) \(x^2-4x+4=\left(x-2\right)^2\)

c) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x-y+3\right)\left(x+y+3\right)\)

Bài 2: 

a) \(101^2-1=\left(101-1\right)\left(101+1\right)=102.100=10200\)

b) \(67^2+66.67+33^2=67^2+2.33.67+33^2\)

\(=\left(67+33\right)^2=100^2=10000\)

Bài 3:

\(x\left(x-3\right)+2\left(x+3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x+2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}\)

Vậy \(x=-2\)hoặc \(x=3\)

B1:

a) \(3x^2-9x=3x.\left(x-3\right)\)

b) \(x^2-4x+4=\left(x-2\right)^2\)

c) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+3+y\right).\left(x+3-y\right)\)

B2:

a) \(101^2-1=\left(101+1\right).\left(101-1\right)=102.100=10200\)

b) \(67^2+66.67+33^2=67^2+2.33.67+33^2=\left(67+33\right)^2=100^2=10000\)

B3:

\(x\left(x-3\right)+2\left(x-3\right)=0\)

\(\left(x-3\right).\left(x+2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x+2=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=3\\x=-2\end{cases}}\)

Chúc bạn học tốt :))

\(\frac{2}{2x+3}+\frac{5}{2x-3}-\frac{2x-33}{9-4x^2}\)

= \(\frac{2}{2x+3}+\frac{5}{2x-3}+\frac{2x-33}{4x^2-9}\)

= \(\frac{2\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)}+\frac{5\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}+\frac{2x-33}{\left(2x-3\right)\left(2x+3\right)}\)

= \(\frac{4x-6+10x-15+2x-33}{\left(2x-3\right)\left(2x+3\right)}\)

= \(\frac{16x-54}{\left(2x-3\right)\left(2x+3\right)}\)

\(\frac{2}{2x+3}+\frac{5}{2x-3}-\frac{2x-33}{9-4x^2}\)\(=\frac{2}{2x+3}+\frac{5}{2x-3}+\frac{2x-33}{4x^2-9}\)

\(=\frac{2\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)}+\frac{5\left(2x+3\right)}{\left(2x+3\right)\left(2x-3\right)}+\frac{2x-33}{\left(2x+3\right)\left(2x-3\right)}\)

\(=\frac{4x-6+10x+15+2x-33}{\left(2x+3\right)\left(2x-3\right)}=\frac{16x-24}{\left(2x+3\right)\left(2x-3\right)}=\frac{8\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)}=\frac{8}{2x+3}\)

Bài 1:

\(A=23^2+46\cdot37+37^2=23^2+2\cdot23\cdot37+37^2=\left(23+37\right)^2=60^2=3600\)

\(B=27^2-44\cdot27+22^2=27^2-2\cdot27\cdot22+22^2=\left(27-22\right)^2=5^2=25\)

Bài 2:

\(A=x^2-4x+5=x^2-4x+4+1=\left(x-2\right)^2+1\)

Vì: \(\left(x-2\right)^2\ge0\) với mọi x

=> \(\left(x-2\right)^2+1\ge1\)

Vậy GTNN của A là 1 khi x=2

\(A=23^2+2.23.37+37^2=\left(23+37\right)^2=60^2=3600\)

\(B=27^2-2.27.22+22^2=\left(27-22\right)^2=5^2=25\)

\(A=x^2-4x+5=\left(x-2\right)^2+1\ge1\)

=> A min=1 khi x=2

a, 1001^2=1001.1001=1001.(1000+1)=1001.1000+1001=1001000+1001=...

b,999^2=999.999=999.(1000-1)=999.1000-999=999000-999=...

c, 22,9.30,1=22,9.(30+0,1)=22,9.30+22,9.0,1=22,9.10.3+2,29=229.3+2,29=687+2,29=689,29 (tui khong biet giau mu len phai viet vay thong cam nhung van dung day)

Ta có : B = 20² - 19² + 18² - 17² + ..... + 2² - 1²

=> B = (20 - 19)(20 + 19) + (18 - 17)(18 + 17) + .....  + (2 - 1)(2 + 1)

=> B = 39 + 35 + 31 + ..... + 3

Số số hạng của dãy trên là : 

                (39 - 3) : 4 + 1 = 10 (số)

Tổng B là : 

              (39 + 3) x 10 : 2 = 210 

                     Vậy B = 210

Ta có : \(C=\left(15^4-1\right)\left(15^4+1\right)-3^8.5^8\)

\(\Rightarrow C=\left(15^4\right)^2-1-15^8\)

\(\Rightarrow C=15^8-1-15^8\)

=> C = -1

Vậy C = - 1

\(a^2+2a+1\)

\(\left(x+2\right)^2\)

\(51^2=\left(50+1\right)^2=50^2+2.50.1+1=2500+100+1=2601\)

\(301^2=300^2+2.300.1+1^2=90000+600+1=90601\)

a) (2x - 3y)² = (2x)² + 2.2x.3y + (3y)² = 4x² + 12xy + 9y²

b) 99² = (100 - 1)² = 100² - 2.100.1 + 1² = 10000 - 200 + 1 = 9801

A) 2²-2.2.3+3²

 = 4-12+9

= 1

B)  =(100-1)²

     = 100²-2.100.1+1²

     = 10000-200+1 

   =9801