Bài 5:
a: \(7x^2-7xy-4x+4y\)
=7x(x-y)-4(x-y)
=(x-y)(7x-4)
b: \(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
c: \(x^3+10x^2+25x-xy^2\)
\(=x\left(x^2+10x+25-y^2\right)\)
\(=x\left[\left(x+5\right)^2-y^2\right]=x\left(x+5+y\right)\left(x+5-y\right)\)
d: \(2x-2y-x^2+y^2\)
\(=2\left(x-y\right)-\left(x-y\right)\left(x+y\right)\)
=(x-y)(2-x-y)
e: \(x^3-4x^2+12x-27\)
\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
f: \(x^2+6x-y^2+9\)
\(=x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2=\left(x+3+y\right)\left(x+3-y\right)\)
h: \(x^3-x^2-4x^2+8x-4\)
\(=x^2\left(x-1\right)-4\left(x^2-2x+1\right)\)
\(=x^2\left(x-1\right)-4\left(x-1\right)^2=\left(x-1\right)\left(x^2-4x+4\right)=\left(x-1\right)\cdot\left(x-2\right)^2\)
i: \(2x^2+4x-30=2\left(x^2+2x-15\right)\)
\(=2\left(x^2+5x-3x-15\right)\)
\(=2\left[x\left(x+5\right)-3\left(x+5\right)\right]=2\left(x+5\right)\left(x-3\right)\)
g: \(x^2+x-6=x^2+3x-2x-6\)
=x(x+3)-2(x+3)
=(x+3)(x-2)
Bài 4:
b: \(x^3-6x^2+12x-8=0\)
=>\(x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3=0\)
=>\(\left(x-2\right)^3=0\)
=>x-2=0
=>x=2
c: \(x^2-16-\left(x-4\right)=0\)
=>(x-4)(x+4)-(x-4)=0
=>(x-4)(x+3)=0
=>\(\left[{}\begin{matrix}x-4=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
Bài 3:
\(a.7x^2-7xy-4x+4y\\ =7x\left(x-y\right)-4\left(x-y\right)\\ =\left(x-y\right)\left(7x-4\right)\\ b.x^2-2x-4y^2-4y\\ =\left(x^2-2x+1\right)-\left(4y^2+4x+1\right)\\ =\left(x-1\right)^2-\left(2y+1\right)^2\\ =\left(x-1-2y-1\right)\left(x-1+2y+1\right)\\ =\left(x-2y-2\right)\left(x+2y\right)\\ c.x^3+10x^2+25x-xy^2\\ =x\left(x^2+10x+25-y^2\right)\\ =x\left[\left(x+5\right)^2-y^2\right]\\ =x\left(x+5-y\right)\left(x+5+y\right)\\ d.2x-2y-x^2+y^2\\ =2\left(x-y\right)-\left(x-y\right)\left(x+y\right)\\ =\left(x-y\right)\left(2-x-y\right)\)
