Bài 1 dễ thì tự làm

Bài 2

\(y^2+2xy-3x-2=0\Leftrightarrow y^2+2xy+x^2=x^2+3x+2\)

\(\Leftrightarrow\left(x+y\right)^2=\left(x+1\right)\left(x+2\right)\)

Vế trái là số chính phương vế phải là tích 2 số nguyên liên tiếp nên 1 trong 2 số x+1 và x+2 phải có 1 số bàng 0

\(\Rightarrow y=-x\)

\(\orbr{\begin{cases}x+1=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-2\end{cases}\Rightarrow\orbr{\begin{cases}y=1\\y=2\end{cases}}}}\)

Vậy \(\left(x;y\right)=\left(-1;1\right);\left(-2;2\right)\)

a)      \(2x\left(5-3x^2\right)-10\left(6+x\right)\)

     \(=10x-6x^3-60-10x\)

     \(=\) \(-6x^3-60\)

a) \(2x\left(5-3x^2\right)-10\left(6+x\right)\\ =2x.5-2x.3x^2-10.6-10.x\\ =10x-6x^3-60-10x\)

b) \(3\left(-x+2\right)-6\left(1-x+5x^{20}\right)\\ =-3.x+3.2-6.1+6.x-5.5x^{20}\\ =-3x+6-6+6x-25x^{20}=25x^{20}+3x\)

c) \(7x\left(2-5x^2+\dfrac{1}{2}x^3\right)-14x\left(1-2x^2\right)\\ =7x.2-7x.5x^2+7x.\dfrac{1}{2}x^3-14x.1+14x.2x^2\\ =14x-25x^3+\dfrac{7}{2}x^4-14x+28x^3=3x^2+\dfrac{7}{2}x^4\) 

b)    \(3\left(-x+2\right)-6\left(1-x+5x^{20}\right)\)

  \(=-3x+6-6+6x-30x^{20}\)

  \(=3x-30x^{20}\)

c) hang dang thuc ( x -y+z)^2

o duoi phan h hang dang thuc luon

a) phan h nhan tu ra sao cho co tử la (x-1)(3x^2 -4x +1)

mau la (x-1)(2x^2 -x-3)

 b ) k nhin dc de

\(\frac{\left(x-y\right)^3+3xy.\left(x+y\right)+y^3}{x-6y}\)

\(=\frac{x^3-3x^2y+3xy^2-y^3+3x^2y+3xy^2+y^3}{x-6y}\)

\(=\frac{x^3+\left(-3x^2y+3x^2y\right)+\left(3xy^2+3xy^2\right)+\left(-y^3+y^3\right)}{x-6y}\)

\(=\frac{x^3+6xy^2}{x-6y}\)

\(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)

\(=\frac{3x^3-3x^2-4x^2+4x+x-1}{2x^3-2x^2+x^2-x-3x+3}\)

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

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

\(=\frac{3x^2-3x-x+1}{2x^2-2x+3x-3}\)

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

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

\(=\frac{3x-1}{2x+3}\)

Bài 1: 

a) \(-5\left(x^2-3x+1\right)+x\left(1+5x\right)=x-2\)

\(\Rightarrow-5x^2+15x-5+x+5x^2=x-2\)

\(\Rightarrow16x-5=x-2\)

\(\Rightarrow16x-x=5-2\)

\(\Rightarrow15x=3\)

\(\Rightarrow x=\dfrac{15}{3}=5\)

b) \(12x^2-4x\left(3x+5\right)=10x-17\)

\(\Rightarrow12x^2-12x^2-20x=10x-17\)

\(\Rightarrow-20x=10x-17\)

\(\Rightarrow-20x-10x=-17\)

\(\Rightarrow-30x=-17\)

\(\Rightarrow x=\dfrac{-30}{-17}=\dfrac{30}{17}\)

c) \(-4x\left(x-5\right)+7x\left(x-4\right)-3x^2=12\)

\(\Rightarrow-4x^2+20x+7x^2-28x-3x^2=12\)

\(\Rightarrow-8x=12\)

\(\Rightarrow x=\dfrac{12}{-8}=-\dfrac{4}{3}\)

Bài 2: 

a) \(\left(x+5\right)\left(x-7\right)-7x\left(x-3\right)\)

\(=x^2-7x+5x-35-7x^2+21x\)

\(=-6x^2+19x-35\)

b) \(x\left(x^2-x-2\right)-\left(x-5\right)\left(x+1\right)\)

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

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

c) \(\left(x-5\right)\left(x-7\right)-\left(x+4\right)\left(x-3\right)\)

\(=x^2-7x-5x+35-x^2-3x+4x-12\)

\(=11x+23\)

d) \(\left(x-1\right)\left(x-2\right)-\left(x+5\right)\left(x+2\right)\)

\(=x^2-2x-x+2-x^2+2x+5x+10\)

\(=4x+12\)