a) A= (5x-2).(x+1)-(x-3).(5x+1)-17(x+3)

=> A= 5x²+5x-2x-2-5x²-x+15x+3-17x-51

=> A= -50

b) B= (6x-5) × ( x+8) - (3x-1) × (2x+3) - 9(4x-3)

=> B= 6x²+48x-5x-40-6x²-9x+2x+3-36x+27

=> B= -10

c) C = x(x³ + x² - 3x -2 ) - ( x² -2 ) × ( x²+x -1 )

=> C= x⁴+x³-3x²-2x-x⁴+x³+3x²-2x-2

=> C= 2x³-4x-2

a: \(B=\left(\dfrac{x+1}{2\left(x-1\right)}+\dfrac{3}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+3}{2\left(x+1\right)}\right)\cdot\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)

\(=\dfrac{x^2+2x+1+6-x^2-2x+3}{2\left(x+1\right)\left(x-1\right)}\cdot\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)

\(=\dfrac{10}{1}\cdot\dfrac{2}{5}=10\cdot\dfrac{2}{5}=4\)

b: \(\dfrac{x^2-36}{2x+10}\cdot\dfrac{3}{6-x}\)

\(=\dfrac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\dfrac{-3}{x-6}\)

\(=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}\)

c: \(\dfrac{5x+10}{4x-8}\cdot\dfrac{4-2x}{x+2}\)

\(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}=\dfrac{-10}{4}=\dfrac{-5}{2}\)

d: \(\dfrac{1-4x^2}{x^2+4x}:\dfrac{2-4x}{3x}\)

\(=\dfrac{1-4x^2}{x\left(x+4\right)}\cdot\dfrac{3x}{2\left(1-2x\right)}\)

\(=\dfrac{\left(1-2x\right)\left(1+2x\right)}{x+4}\cdot\dfrac{3}{2\left(1-2x\right)}=\dfrac{3\left(2x+1\right)}{x+4}\)

Cái này dễ mà, nên tự làm đi 😂😂😂

1.

a) \(5x.5x.5x=\left(5x\right)^3.\)

b) \(x^1.x^2.....x^{2006}=x^{\frac{\left(2006+1\right).2006}{2}=}x^{2013021}.\)

c) \(x^1.x^4.x^7.....x^{100}=x^{\frac{\left(100+1\right).\left(\frac{100-1}{3}+1\right)}{2}}=x^{1717}.\)

d) \(x^2.x^5.x^8.....x^{2003}=x^{\frac{\left(2003+2\right).\left(\frac{2003-2}{3}+1\right)}{2}}=x^{669670}.\)

2.

\(2^x+80=3^y\)

Với \(x>0\Rightarrow2^x\) chẵn

Và 80 chẵn

\(\Rightarrow2^x+80\) chẵn.

Mà \(3^y\) lẻ

\(\Rightarrow x< 0.\)

Mà \(x\in N\)

\(\Rightarrow x=0.\)

\(\Rightarrow2^0+80=3^y\)

\(\Rightarrow1+80=3^y\)

\(\Rightarrow3^y=81\)

\(\Rightarrow3^y=3^4\)

\(\Rightarrow y=4.\)

Vậy \(\left(x;y\right)=\left(0;4\right).\)

Chúc bạn học tốt!

1.viết tích dưới dạng lũy thừa

a.5x.5x.5x

=(5x)\(^3\)

b.x\(^1\) . x \(^2\).......x \(^{2006}\)

=x \(^{2013021}\)

c.x\(^1\).x \(^4\) .x \(^7\)......x \(^{100}\)

=x \(^{1717}\)

d.x \(^2\) .x \(^5\).x \(^8\).......x\(^{2003}\)

=x \(^{669670}\)

2 \(^x\)+80=3\(^y\)

ta có 3\(^y\)lẻ nên 2 \(^x\)+80 lẻ .

Với x \(\ge\)1

thì 2 \(^x\)+80 chẵn không thỏa mãn

nên x=0

=>1+80=3\(^y\)

=>81=3\(^y\)

=>3\(^4\)=3\(^y\)

=>y=4

Tìm x:

a,3(x-5)-x+5=0

=>3(x-5)-(x-5)=0

=>(x-5)(3-1)=0

=>(x-5).2=0

=>x-5=0

=>x=5

Vậy x=5.

Câu 2: 

\(2\left(3x-4\right)-3\left(2x+3\right)+\left(3-5x\right)-\left(-4x+2\right)=0\)

\(\Leftrightarrow6x-8-6x-9+3-5x+4x-2=0\)

=>-x-16=0

=>x=-16