Bài 2:

1: \(\left(2x-1\right)^2-4\left(2x-1\right)=0\)

=>\(\left(2x-1\right)\left(2x-1-4\right)=0\)

=>(2x-1)(2x-5)=0

=>\(\left[{}\begin{matrix}2x-1=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)

2: \(9x^3-x=0\)

=>\(x\left(9x^2-1\right)=0\)

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

=>\(\left[{}\begin{matrix}x=0\\3x-1=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\end{matrix}\right.\)

3: \(\left(3-2x\right)^2-2\left(2x-3\right)=0\)

=>\(\left(2x-3\right)^2-2\left(2x-3\right)=0\)

=>(2x-3)(2x-3-2)=0

=>(2x-3)(2x-5)=0

=>\(\left[{}\begin{matrix}2x-3=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)

4: \(\left(2x-5\right)\left(x+5\right)-10x+25=0\)

=>\(2x^2+10x-5x-25-10x+25=0\)

=>\(2x^2-5x=0\)

=>\(x\left(2x-5\right)=0\)

=>\(\left[{}\begin{matrix}x=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{2}\end{matrix}\right.\)

Bài 1:

1: \(3x^3y^2-6xy\)

\(=3xy\cdot x^2y-3xy\cdot2\)

\(=3xy\left(x^2y-2\right)\)

2: \(\left(x-2y\right)\left(x+3y\right)-2\left(x-2y\right)\)

\(=\left(x-2y\right)\cdot\left(x+3y\right)-2\cdot\left(x-2y\right)\)

\(=\left(x-2y\right)\left(x+3y-2\right)\)

3: \(\left(3x-1\right)\left(x-2y\right)-5x\left(2y-x\right)\)

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

\(=(x-2y)(3x-1+5x)\)

\(=\left(x-2y\right)\left(8x-1\right)\)

4: \(x^2-y^2-6y-9\)

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

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

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

5: \(\left(3x-y\right)^2-4y^2\)

\(=\left(3x-y\right)^2-\left(2y\right)^2\)

\(=\left(3x-y-2y\right)\left(3x-y+2y\right)\)

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

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

6: \(4x^2-9y^2-4x+1\)

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

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

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

8: \(x^2y-xy^2-2x+2y\)

\(=xy\left(x-y\right)-2\left(x-y\right)\)

\(=\left(x-y\right)\left(xy-2\right)\)

9: \(x^2-y^2-2x+2y\)

\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)

\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-2\right)\)

4x(x-2y)+8y(2y-x)

=4x(x-2y)-8y(x-2y)

=(4x-8y)(x-2y)

=4(x-2y)(x-2y)

=4(x-2y)^2

\(4x\left(x-2y\right)+8y\left(2y-x\right)\)

\(=\left(x-2y\right)\left(4x-8y\right)\)

\(=\left(x-2y\right)\left(x-2y\right).4\)\(=\left(x-2y\right)^2\)

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

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

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

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

\(4x\left(x-2y\right)-8y\left(x-2y\right)\\ =\left(x-2y\right)\left(4x-8y\right)\\ =\left(x-2y\right)\cdot4\left(x-2y\right)\)

tách nhỏ câu hỏi ra bạn

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

\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)

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

\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

\(x\left(x+2\right)\left(x+3\right)\left(x+5\right)+9\)

\(=\left(x^2+5x+6\right)\left(x^2+5x\right)+9\)

Đặt \(t=x^2+5x\)ta được;

\(t\left(t+6\right)+9=t^2+6t+9\)

\(=\left(t+3\right)^2=\left(x^2+5x+3\right)^2\)

b)\(x^2+2xy+y^2+2x+2y-15\)

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

\(=\left(x+y+1+4\right)\left(x+y+1-4\right)\)

\(=\left(x+y-3\right)\left(x+y+5\right)\)

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

đáp án: a là đúng

A

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

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

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

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

h ) \(x^2-ax^2-y+ay+cx^2-cy\)

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

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

b  \(x^8y^8+x^4y^4+1=x^8y^8+2x^4y^4+1-x^4y^4=\left(x^4y^4\right)^2+2x^4y^4+1-\left(x^2y^2\right)^2\)

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

c  \(x^2y+xy^2+xz^2+x^2z+y^2z+yz^2+2xyz=\left(x^2y+x^2z+xyz+xy^2\right)+\left(xz^2+yz^2+xyz+y^2z\right)\)

\(=x\left(xy+xz+yz+y^2\right)+z\left(xz+yz+xy+y^2\right)=\left(x+z\right)\left(xy+xz+yz+y^2\right)\)

\(=\left(x+z\right)\left(x\left(y+z\right)+y\left(y+z\right)\right)=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)

a  \(3xyz+x\left(y^2+z^2\right)+y\left(x^2+z^2\right)+z\left(x^2+y^2\right)=3xyz+xy^2+xz^2+x^2y+yz^2+x^2z+y^2z\)

\(=\left(x^2y+x^2z+xyz\right)+\left(xy^2+xyz+y^2z\right)+\left(xyz+xz^2+yz^2\right)\)

\(=x\left(xy+xz+yz\right)+y\left(xy+xz+yz\right)+z\left(xy+xz+yz\right)=\left(x+y+z\right)\left(xy+xz+yz\right)\)

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

=(2x-y)(x-y)-(2x-y)(2y-3x)-(4x-3y)²

=(2x-3y)(x-y-2y+3x)-(4x-3y)²

=(2x-3y)(4x-3y)-(4x-3y)²

^{=(4x-3y)(2x-3y-4x+3y)}

=(4x-3y))(-2x)