a) 125 x 6 = ...6... × 125

b) 34 × (4 + 5) = 9 × ..34..

c) 18 x 1000=18000

d) 9000 : 100=90

a) 125 x 6 = ...6.. × 125

b) 34 × (4 + 5) = 9 × ..34..

c) 18 x 1000= 18000

d) 9000 : 100= 90

a) 6

b) 34

c) 18 000

d) 90

a)

\(\left[\left(x-81\right)^3:5^3\right]-2^3=0\\ =>\left(x-81\right)^3:5^3=2^3\\ =>\left(x-81\right)^3=2^3.5^3=10^3\\ =>x-81=10\\ =>x=91\)

b) 

\(3^{n+1}.3^{n+3}=18^{10}:6^{10}\\ =>3^{n+1+n+3}=3^{10}\\ =>2n+4=10\\ =>2n=6=>n=3\)

a) \(\left[\left(x+81\right)^3:5^3\right]-2^3=0\)

\(\Rightarrow\left(\dfrac{x+81}{5}\right)^3=2^3\)

\(\Rightarrow\dfrac{x-81}{5}=2\)

\(\Rightarrow x-81=10\)

\(\Rightarrow x=91\)

b) \(3^{n+1}\cdot3^{n+3}=18^{10}:6^{10}\)

\(\Rightarrow3^{2n+4}=3^{10}\)

\(\Rightarrow2n+4=10\)

\(\Rightarrow2n=6\)

\(\Rightarrow n=3\)

\(\text{a) -3000 : 2 + 5(2x-1) = 125}\\ -1500+5\left(2x-1\right)=125\\ 5\left(2x-1\right)=125-\left(-1500\right)\\ 5\left(2x-1\right)=1625\\ 2x-1=1625:5\\ 2x-1=325\\ 2x=325+1\\ 2x=326\\ x=326:2\\ x=163\)

\(\text{b) 6x -12 = -18}\\ 6x=-16+12\\ 6x=-6\\ x=-1\)

\(\text{c) 17 + 3(x-1) = 5}\\ 3\left(x-1\right)=5-17\\ 3\left(x-1\right)=-12\\ x-1=-12:3\\ x-1=-4\\ x=-3\)

\(a,=3\sqrt{5}-2\sqrt{5}-\sqrt{5}+5\sqrt{5}=5\sqrt{5}\\ b,=9\sqrt{a}-6\sqrt{a}-\sqrt{a}=2\sqrt{a}\\ c,Sửa:3\sqrt[3]{27}-3\sqrt[3]{-8}-3\sqrt[3]{-125}\\ =3\cdot3-3\left(-2\right)-3\left(-5\right)\\ =9+6+15=30\)

\(a,\\ \left(x+\dfrac{1}{2}\right)^3=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\ \left(x+\dfrac{1}{2}\right)^3=\left(\dfrac{2}{5}\right)^3\\ \Rightarrow\left(x+\dfrac{1}{2}\right)=\dfrac{2}{5}\\ x=\dfrac{2}{5}-\dfrac{1}{2}\\ x=-\dfrac{1}{10}\)

\(b,3\left|x\right|-27=\dfrac{1}{5}\\ 3\left|x\right|=\dfrac{1}{5}+27\\ 3\left|x\right|=\dfrac{136}{5}\\ \left|x\right|=\dfrac{136}{5}:3\\ \left|x\right|=\dfrac{136}{15}\\ Vậy:x=\dfrac{136}{15}.or.x=-\dfrac{136}{15}\)

\(c,\\ \dfrac{1}{2}.\left(x+\dfrac{1}{3}\right)=\dfrac{1}{16}\\ \left(x+\dfrac{1}{3}\right)=\dfrac{1}{16}:\dfrac{1}{2}\\ \left(x+\dfrac{1}{3}\right)=\dfrac{1}{8}\\ x=\dfrac{1}{8}-\dfrac{1}{3}\\ x=-\dfrac{5}{24}\)

a) \(8x^3-\dfrac{1}{27}=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2}{3}x+\dfrac{1}{9}\right)\)

b) \(\dfrac{1}{8}a^3-125b^6=\left(\dfrac{1}{2}a-5b^2\right)\left(\dfrac{1}{4}a+\dfrac{5}{2}ab^2+25b^4\right)\)

c) \(125+\left(a-b\right)^3=\left(5+a-b\right)\left(25-5a+5b+a^2-2ab+b^2\right)\)

Bài 3: 

a: \(=\left(2x-5\right)\left(4x^2+10x+25\right)\)

\(a,=-2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\sqrt{5}=-18\sqrt{5}\)

\(b,=2\sqrt{3}-5\sqrt{3}+4\sqrt{3}-7\sqrt{3}=-6\sqrt{3}\)

\(c,=3\sqrt{3}+7\sqrt{3}-9\sqrt{3}+11\sqrt{3}=12\sqrt{3}\)

a) Ta có: \(-\sqrt{20}+3\sqrt{45}-6\sqrt{80}-\dfrac{1}{5}\sqrt{125}\)

\(=-2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\dfrac{1}{5}\cdot5\sqrt{5}\)

\(=-17\sqrt{5}-\sqrt{5}=-18\sqrt{5}\)

b) Ta có: \(2\sqrt{3}-\sqrt{75}+2\sqrt{12}-\sqrt{147}\)

\(=2\sqrt{3}-5\sqrt{3}+4\sqrt{3}-7\sqrt{3}\)

\(=-6\sqrt{3}\)

\(a,\Rightarrow3x-1=5\\ \Rightarrow3x=6\\ \Rightarrow x=2\\ b,\Rightarrow15\left(x+1\right)=200-35=165\\ \Rightarrow x+1=11\\ \Rightarrow x=10\\ c,\Rightarrow x\inƯC\left(18,54\right)=Ư\left(18\right)=\left\{1;2;3;6;9;18\right\}\)

a) 8x³ - 125=(2x)³-5³=(2x-5)(2x+5)

b) 1 - 27x³y⁶=1-3³x³(y²)³=1-(3xy²)³=(1-3xy²)(1-3xy²+9x²y⁴)

c)27x³ + y³/64=(3x)³ + y³/4³=(3x)³ + (y/4)³=(3x+y/4)(9x²-3xy/4+y²/16)

d) 27x³ + 125y³ = (3x)³+(5y)³=(3x+5y)(9x²-15xy+25y²)