\(\left(2x-3\right)\left(x+5\right)-x\left(2x+7\right)\\ =2x^2-3x+10x-15-2x^2-7x\\ =\left(2x^2-2x^2\right)+\left(10x-3x-7x\right)-15\\ =-15\)

-15

\(\left(2x-3\right)\left(x+5\right)-x\left(2x+7\right)\\ =2x^2+10x-3x-15-2x^2-7x\\ =-15\)

`6\sqrt(2/3)-\sqrt(24)+2\sqrt(3/8)+2\sqrt(1/6)`

`=6. \sqrt6/3 - \sqrt(2^2 .6) + 2. \sqrt(24)/8 + 2. \sqrt6/6`

`=2\sqrt6-2\sqrt6+ \sqrt6/2 + \sqrt6/3`

`=\sqrt6/2+\sqrt6/3`

`=(3\sqrt6+2\sqrt6)/6`

`=(5\sqrt6)/6`

Ta có: \(6\sqrt{\dfrac{2}{3}}-\sqrt{24}+2\sqrt{\dfrac{3}{8}}+2\sqrt{\dfrac{1}{6}}\)

\(=\dfrac{6\sqrt{2}}{\sqrt{3}}-2\sqrt{6}+2\cdot\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{2}{\sqrt{6}}\)

\(=2\sqrt{6}-2\sqrt{6}+\dfrac{\sqrt{3}}{\sqrt{2}}+\dfrac{\sqrt{2}}{\sqrt{3}}\)

\(=\dfrac{\sqrt{6}}{2}+\dfrac{\sqrt{6}}{3}=\dfrac{5\sqrt{6}}{6}\)

\(A=2^2+2^2+2^3+...+2^{2021}\\ 2A=2^3+2^3+2^4+...+2^{2022}\\ A=2^{2022}+2^3-2^2-2^2\)

\(2A=8+2^3+...+2^{2022}\)

\(\Leftrightarrow A=2^{2022}+8-4-2^2=2^{2022}\)

20/24

31/40

10/3

20/24

31/40

10/3

 a)\(=\dfrac{20}{24}=\dfrac{5}{6}\)

b)\(=\dfrac{31}{40}\)

c)\(=\dfrac{24}{12}+\dfrac{9}{12}+\dfrac{7}{12}=\dfrac{40}{12}=\dfrac{10}{3}\)

a: \(=6\sqrt{2}-12\sqrt{3}-10\sqrt{2}+12\sqrt{3}=-4\sqrt{2}\)

b: \(=\sqrt{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}=\sqrt{4-3}=1\)

= 4x^2 + 20x + 25 + 3x^2 - 12

= x^2 + 20x + 13

\(P=\frac{3^{2010}-6^{2010}+9^{2010}-12^{2010}+15^{2010}-18^{2010}}{-1+2^{2010}-3^{2010}+4^{2010}-5^{2010}+6^{2010}}\)

\(P=\frac{-3^{2010}.\left(-1+2^{2010}-3^{2010}+4^{2010}-5^{2010}+6^{2010}\right)}{-1+2^{2010}-3^{2010}+4^{2010}-5^{2010}+6^{2010}}\)

\(P=-3^{2010}\)

\(E^3=182+\sqrt{33125}+182-\sqrt{33125}+3\sqrt[3]{182^2-33125}\left(E\right)\)

   =\(364-3E\)

\(\Rightarrow E^3+3E-364=0\) 

\(\Leftrightarrow E^3-7E^2+7E^2-49E+52E-364=0\)

\(\Leftrightarrow\left(E-7\right)\left(E^2+7E+52\right)=0\)

\(\Rightarrow E=7\)

ta có \(E^3=\left(\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\right)^3\)

\(E^3=\left(182+\sqrt{33125}\right)+\left(182-\sqrt{33125}\right)+3\cdot E\cdot\sqrt[3]{33124-33125}\)

\(E^3=364-3E\)

giải phương trình \(E^3+3E-364=0\)

suy ra E= 7