Bài 4:
a: \(3x+x^2-4=0\)
=>\(x^2+3x-4=0\)
=>\(x^2+4x-x-4=0\)
=>\(x\left(x+4\right)-\left(x+4\right)=0\)
=>\(\left(x+4\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
b: \(x^2-7x+6=0\)
=>\(x^2-x-6x+6=0\)
=>\(x\left(x-1\right)-6\left(x-1\right)=0\)
=>\(\left(x-1\right)\left(x-6\right)=0\)
=>\(\left[{}\begin{matrix}x-1=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=6\end{matrix}\right.\)
c: \(3x^2+10x-13=0\)
=>\(3x^2+13x-3x-13=0\)
=>\(x\left(3x+13\right)-\left(3x+13\right)=0\)
=>\(\left(3x+13\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}3x+13=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{13}{3}\end{matrix}\right.\)
d: \(x^3-16x=0\)
=>\(x\left(x^2-16\right)=0\)
=>\(x\left(x-4\right)\left(x+4\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
Bài 3:
a: \(3x-3y+x^2-y^2\)
\(=\left(3x-3y\right)+\left(x^2-y^2\right)\)
\(=3\left(x-y\right)+\left(x+y\right)\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+3\right)\)
b: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
c: \(x^6-x^4+2x^3+2x^2\)
\(=x^2\left(x^4-x^2+2x+2\right)\)
\(=x^2\left[x^2\left(x^2-1\right)+2\left(x+1\right)\right]\)
\(=x^2\cdot\left[x^2\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\right]\)
\(=x^2\cdot\left(x+1\right)\left(x^3-x^2+2\right)\)
d: \(x^3-3x^2+3x-1-y^3\)
\(=\left(x^3-3x^2+3x-1\right)-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\)
\(=\left(x-y-1\right)\left(x^2-2x+1+xy-y+y^2\right)\)
