b. \(\dfrac{4.2.3.5.2.6.2.5.3}{4.3.4.5.6.4.5.6}=\dfrac{1}{4}\)

c. \(\dfrac{17.2.101.2005}{17.2.101.2.2005}=\dfrac{1}{2}\)

d. \(\dfrac{2.3.4.2.11.13.17}{3.11.4.4.17.13.2}=\dfrac{1}{2}\)

a)\(\dfrac{4\times6\times10\times12\times15}{4\times12\times5\times24\times30}=\dfrac{2}{2\times2\times2}=\dfrac{2}{8}=\dfrac{1}{4}\)

b)\(\dfrac{34\times101\times2005}{17\times202\times4010}=\dfrac{2}{2\times2}=\dfrac{2}{4}=\dfrac{1}{2}\)

c)\(\dfrac{6\times8\times11\times13\times17}{33\times16\times17\times26}=\dfrac{6}{3\times2\times2}=\dfrac{1}{2}\)

11 x 12 + 12 x 13 + 13 x 14 + 14 x 15 + 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + 20 x 21

= 12 x ( 11 + 13 ) + 14 x ( 13 + 15 ) + 16 x ( 15 + 17 ) + 18 x ( 17 + 19 ) + 20 x 21

= 12 x 24 + 14 x 28 + 16 x 32 + 18 x 36 + 420

= 288 + 392 + 512 + 648 + 420

= ( 288 + 392 ) + ( 512 + 648 ) + 420 

= 680 + 1160 + 420

= 1840 + 420

= 2260

tk nha

= 

Ta có:

    11 x 12 + 12 x 13 + 13 x 14 + 14 x 15 + 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + 20 x 21

= 12 x ( 11 + 13 ) + 14 x ( 13 + 15 ) + 16 x ( 15 + 17 ) + 18 x ( 17 + 19 ) + 20 x 21

= 12 x 24 + 14 x 28 + 16 x 32 + 18 x 36 + 420

= 288 + 392 + 512 + 648 + 420

= ( 288 + 392 ) + ( 512 + 648 ) + 420 

= 680 + 1160 + 420

= 1840 + 420

= 2260

#Mạt Mạt#

   11 x 12 + 12 x 13 + 13 x 14 + 14 x 15 + 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + 20 x 21

= 12 x ( 11 + 13 ) +  14 x ( 13 + 15 ) + 16 x ( 15 + 17 ) + 18 x ( 17 + 19 ) + 20 x ( 19 + 21 )

= 12 x 24 + 14 x 28 + 16 x 32 + 18 x 36 + 20 x 40

= 288 + 392 + 512 + 648 + 800

= ( 288 + 392 ) + ( 512 + 648 ) + 800

= 680 + 1160 + 800

= 2640

a,\(2,5.16,27.4+7,3=16,27.10+7,3=162,7+7,3=170\)

b,\(8.6.10+4.25.12+3.16.31+2.34.24=48.10+48.25+48.31+48.34\)

\(=48.\left(10+25+31+34\right)=48.100=4800\)

c,\(78.31+78.24+78.17+22.72=78\left(31+24+17\right)+22.72=78.72+22.72\)

\(=72.\left(78+22\right)=72.100=7200\)

d,\(102.67-34.51=102.67-17.102=102.\left(67-17\right)=102.50=5100\)

đéo hiểu thì cút nhé đéo ai khiến m trả lời cả . ngu thì nói ngu đi đừng bày đặt t ghét nhất là cái loại như m đấy ạ 

Bài 2 

a, \(1-\left(12,5+x-4,25\right):21,75=0\)

\(=>21,75-12,5-x+4,25=0\)

\(=>13,5-x=0=>x=13,5\)

b,\(x.101-x+72.99+72=21050\)

\(=>100x+72.100=21050\)

\(=>100\left(x+72\right)=21050\)

\(=>x+72=210,5\)\(=>x=138,5\)

c,\(151-2\left(x-6\right)=2227:17\)

\(=>151-2\left(x-6\right)=131\)

\(=>2\left(x-6\right)=20\)

\(=>2x=32=>x=16\)

d,\(\left(x+4\right)+\left(x+6\right)+\left(x+8\right)+...+\left(x+26\right)=210\)\(=>12x+\left(4+6+8+...+26\right)=210\)

\(=>12x+180=210=>12x=30\)

\(=>x=\frac{30}{12}=\frac{15}{6}=\frac{5}{2}\)

1)  \(x^2-7x+6=x^3+1-7x-7=\left(x^3+1\right)-7\left(x+1\right)=\left(x+1\right)\left(x^2-x-6\right)\)

2)  \(x^3-9x^2+6x+16\)

\(\left(x^3+1\right)-\left[\left(9x^2-6x+1\right)-16\right]\)

\(=\left(x^3+1\right)-\left[\left(3x-1\right)^2-16\right]=\left(x^3+1\right)-\left(3x-1+4\right)\left(3x-1-4\right)\)\(=\left(x^3+1\right)-3\left(3x-5\right)\left(x+1\right)\)\(=\left(x+1\right)\left[x^2-x+1-9x+15\right]=\left(x+1\right)\left(x^2-10x+16\right)\)

\(=\left(x+1\right)\left[x\left(x-2\right)-8\left(x-2\right)\right]\)\(\left(x+1\right)\left(x-2\right)\left(x-8\right)\)

3)   \(x^3-6x^2-x+30\)

\(=x^3-5x^2-x^2+5x-6x+30\)

\(=x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)

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

4)  \(2x^3-x^2+5x+3=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)

\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)

\(=\left(2x+1\right)\left(x^2-x+3\right)\)

5) \(27x^3-27x^2+18x-4=\left(27x^3-1\right)-\left(27x^2-18x+3\right)\)

\(=\left(3x-1\right)\left(9x^2+3x+1\right)-3\left(9x^2-6x+1\right)\)

\(=\left(3x-1\right)\left(9x^2+3x+1\right)-3\left(3x-1\right)^2\)

\(=\left(3x-1\right)\left(9x^2+3x+1-9x+3\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)

gửi phần này trước còn lại làm sau !!! tk mk nka !!!

nhiều thế

6) \(\left(x+y\right)^2-\left(x+y\right)-12\)\(=\left(x+y\right)^2-2\cdot\frac{1}{2}\left(x+y\right)+\frac{1}{4}-\frac{49}{4}\)

\(=\left(x+y-\frac{1}{2}\right)^2-\left(\frac{7}{2}\right)^2\)\(=\left(x+y-\frac{1}{2}-\frac{7}{2}\right)\left(x+y-\frac{1}{2}+\frac{7}{2}\right)\)

\(=\left(x-4\right)\left(x+3\right)\)

7)   \(\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)          (NHÂN x + 2 vs x +  5  và  x + 3 vs x + 4 )

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

ĐẶT   \(x^2+7x+11=y\)   ta được :  

\(\left(y+1\right)\left(y-1\right)-24=y^2-1-24\)

\(=y^2-25=\left(y-5\right)\left(y+5\right)\)

8)  \(4x^4-32x^2+1=4x^4+4x^2+1-36x^2\)

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

9) sai đề rùi bạn ơi ! đề đúng nè 

\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

Ta thấy :  

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

Thay vào biểu thức bài cho ta được : 

\(3\left(x^2-x+1\right)\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)

\(=\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\)

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

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

bài ở trên câu 3 : kết luận là  \(\left(x-3\right)\left(x^2-x-6\right)\)bạn sửa lại giúp mk nka !!! Th@nk !!! Tk Mk vs  

Bài 1

a) \(5\times72\times10\times2=\left(5\times2\times10\right)\times72=100\times72=7200\) 

b) \(40\times125=5\times\left(8\times125\right)=5\times1000=5000\) 

c) \(16\times6\times25=4\times4\times6\times25=\left(4\times6\right)\times\left(4\times25\right)=24\times100=2400\) Bài 2:

a) \(24\times57+43\times24=24\times\left(57+43\right)=24\times100=2400\) 

b) \(12\times19+80\times12+12=12\times\left(19+80+1\right)=12\times100=1200\) 

c) \(\left(36\times15\times169\right)\div\left(5\times18\times13\right)\) 

 \(=\left(18\times2\times3\times5\times13\times13\right)\div\left(5\times18\times13\right)\) 

\(=\left(2\times3\times13\right)\times\left(18\times5\times13\right)\div\left(5\times18\times13\right)\) 

\(=2\times3\times13\)

\(=78\)

d) \(\left(44\times52\times60\right)\div\left(11\times13\times15\right)\) 

\(=\left(4\times11\times4\times13\times4\times15\right)\div\left(11\times13\times15\right)\)

\(=\left(4\times4\times4\right)\times\left(11\times13\times15\right)\div\left(11\times13\times15\right)\)

\(=4\times4\times4\)

\(=64\)

Bài 3:

a) \(x-280\div35=5\times54\) 

                \(x-8=270\) 

                      \(x=270+8\) 

                      \(x=278\) 

b) \(\left(x-280\right)\div35=54\div4\) 

    \(\left(x-280\right)\div35=\dfrac{27}{2}\) 

               \(x-280=\dfrac{27}{2}\times35\) 

                \(x-280=\dfrac{945}{2}\) 

                          \(x=\dfrac{945}{2}+280\) 

                          \(x=\dfrac{1505}{2}\) 

c) \(\left(x-128+20\right)\div192=0\) 

                 \(x-128+20=0\times192\) 

                \(x-128+20=0\) 

                        \(x-128=0-20\) 

                        \(x-128=-20\)

                                  \(x=-20+128\) 

                                 \(x=108\) 

d) \(4\times\left(x+200\right)=460+85\times4\) 

    \(4\times\left(x+200\right)=460+340\) 

    \(4\times\left(x+200\right)=800\) 

             \(x+200=800\div4\) 

             \(x+200=200\) 

                      \(x=200-200\) 

                      \(x=0\) 

Bài 4:

a) \(\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}\) 

b) \(\dfrac{8}{11}+\dfrac{19}{11}=\dfrac{27}{11}\) 

c) \(\dfrac{3}{8}+\dfrac{5}{12}=\dfrac{9}{24}+\dfrac{10}{24}=\dfrac{19}{24}\) 

d) \(\dfrac{3}{4}+\dfrac{7}{12}=\dfrac{9}{12}+\dfrac{7}{12}=\dfrac{16}{12}=\dfrac{4}{3}\) 

Bài 5:

a) \(x-\dfrac{6}{7}=\dfrac{5}{2}\) 

           \(x=\dfrac{5}{2}+\dfrac{6}{7}\) 

           \(x=\dfrac{47}{14}\) 

b) \(\dfrac{12}{7}\div x+\dfrac{2}{3}=\dfrac{7}{5}\) 

            \(\dfrac{12}{7}\div x=\dfrac{7}{5}-\dfrac{2}{3}\) 

             \(\dfrac{12}{7}\div x=\dfrac{11}{15}\) 

                       \(x=\dfrac{12}{7}\div\dfrac{11}{15}\) 

                        \(x=\dfrac{180}{77}\)

a) x = 4

b) x = 3

c) x = 2

d) x = 1

e) x = 3

f) x = 2

g) x = 4

h) x = 3

a,\(x^3-7x+6\)

\(=x^3-2x^2+2x^2-4x-3x+6\)

\(=\left(x^3-2x^2\right)+\left(2x^2-4x\right)-\left(3x-6\right)\)

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

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

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

\(=\left(x-2\right).\left[\left(x^2-x\right)+\left(3x-3\right)\right]\)

\(=\left(x-2\right).\left[x.\left(x-1\right)+3.\left(x-1\right)\right]\)

\(=\left(x-2\right).\left(x-1\right).\left(x+3\right)\)

b,\(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=\left(x^3-8x^2\right)-\left(x^2-8x\right)-\left(2x-16\right)\)

\(=x^2.\left(x-8\right)-x.\left(x-8\right)-2.\left(x-8\right)\)

\(=\left(x-8\right).\left(x^2-x-2\right)\)

\(=\left(x-8\right).\left(x^2+x-2x-2\right)\)

\(=\left(x-8\right).\left[\left(x^2+x\right)-\left(2x+2\right)\right]\)

\(=\left(x-8\right).\left[x.\left(x+1\right)-2.\left(x+1\right)\right]\)

\(=\left(x-8\right).\left(x+1\right).\left(x-2\right)\)

c,\(x^3-6x^2-x+30\)

\(=x^3-5x^2-x^2+5x-6x+30\)

\(=\left(x^3-5x^2\right)-\left(x^2-5x\right)-\left(6x-30\right)\)

\(=x^2.\left(x-5\right)-x.\left(x-5\right)-6.\left(x-5\right)\)

\(=\left(x-5\right).\left(x^2-x-6\right)\)

\(=\left(x-5\right).\left(x^2+2x-3x-6\right)\)

\(=\left(x-5\right).\left[\left(x^2+2x\right)-\left(3x+6\right)\right]\)

\(=\left(x-5\right).\left[x.\left(x+2\right)-3.\left(x+2\right)\right]\)

\(=\left(x-5\right).\left(x+2\right).\left(x-3\right)\)

Chúc bạn học tốt!!!

d,\(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

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

\(=x^2.\left(2x+1\right)-x.\left(2x+1\right)+3.\left(2x+1\right)\)

\(=\left(2x+1\right).\left(x^2-x+3\right)\)

e, \(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=\left(27x^2-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)

\(=9x^2.\left(3x-1\right)-6x.\left(3x-1\right)+4.\left(3x-1\right)\)

\(=\left(3x-1\right).\left(9x^2-6x+4\right)\)

Chúc bạn học tốt!!!

7, \(\left(x+2\right).\left(x+3\right).\left(x+4\right).\left(x+5\right)-24\)

\(=\left[\left(x+2\right).\left(x+5\right)\right].\left[\left(x+3\right).\left(x+4\right)\right]-24\)

\(=\left(x^2+5x+2x+10\right).\left(x^2+4x+3x+12\right)-24\)

\(=\left(x^2+7x+10\right).\left(x^2+7x+12\right)-24\)(1)

Đặt \(t=x^2+7x+10\Rightarrow t+2=x^2+7x+12\)

\(\Rightarrow\left(1\right)=t.\left(t+2\right)-24\)

\(=t^2+2t-24=t^2-4t+6t-24\)

\(=\left(t^2-4t\right)+\left(6t-24\right)=t.\left(t-4\right)+6.\left(t-4\right)\)

\(=\left(t-4\right).\left(t+6\right)\) (2)

Vì \(t=x^2+7x+10\) nên:

(2) \(=\left(x^2+7x+10-4\right).\left(x^2+7x+10+6\right)\)

\(=\left(x^2+7x+6\right).\left(x^2+7x+16\right)\)

\(=\left(x^2+x+6x+6\right).\left(x^2+7x+16\right)\)

\(=\left[\left(x^2+x\right)+\left(6x+6\right)\right].\left(x^2+7x+16\right)\)

\(=\left[x.\left(x+1\right)+6.\left(x+1\right)\right].\left(x^2+7x+16\right)\)

\(=\left(x+1\right).\left(x+6\right).\left(x^2+7x+16\right)\)

Chúc bạn học tốt!!!

a) \(\dfrac{25}{37}\times\dfrac{18}{29}+\dfrac{18}{29}\times\dfrac{12}{37}\)

\(=\dfrac{18}{29}\times\left(\dfrac{25}{37}+\dfrac{12}{37}\right)\)

\(=\dfrac{18}{29}\times\dfrac{37}{37}\)

\(=\dfrac{18}{29}\times1\)

\(=\dfrac{18}{29}\)

b) \(\dfrac{31}{85}\times\dfrac{11}{19}+\dfrac{31}{85}\times\dfrac{12}{19}-\dfrac{42}{19}\times\dfrac{31}{85}\)

\(=\dfrac{31}{85}\times\left(\dfrac{11}{19}+\dfrac{12}{19}-\dfrac{42}{19}\right)\)

\(=\dfrac{31}{85}\times\dfrac{-19}{19}\)

\(=\dfrac{31}{85}\times-1\)

\(=-\dfrac{31}{85}\)

c) \(\dfrac{16}{53}:\dfrac{17}{9}-\dfrac{16}{53}:\dfrac{17}{8}\)

\(=\dfrac{16}{53}:\left(\dfrac{9}{17}-\dfrac{8}{17}\right)\)

\(=\dfrac{16}{53}:\dfrac{1}{17}\)

\(=\dfrac{16}{901}\)

c) \(\dfrac{1}{5}\times\dfrac{12}{31}\times\dfrac{4}{3}+\dfrac{19}{31}\times\dfrac{4}{15}\)

\(=\dfrac{4}{15}\times\dfrac{12}{31}+\dfrac{19}{31}\times\dfrac{4}{15}\)

\(=\dfrac{4}{15}\times\left(\dfrac{12}{31}+\dfrac{19}{31}\right)\)

\(=\dfrac{4}{15}\times\dfrac{31}{31}\)

\(=\dfrac{4}{15}\times1\)

\(=\dfrac{4}{15}\)

a: =18/29*(25/37+12/37)

=18/29

b: =31/85(11/19+12/19-42/19)

=-31/85

c; =16/53(9/17+8/17)=16/53

d: =4/15(12/31+19/31)=4/15