\(x^4+6x^3+13x^2+12x+4\)

\(=x^4+x^3+5x^3+5x^2+8x^2+8x+4x+4\)

\(=x^3\left(x+1\right)+5x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3+5x^2+8x+4\right)\)

\(=\left(x+1\right)\left(x^3+x^2+4x^2+4x+4x+4\right)\)

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

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

a) Ta có: \(x^2-2xy+y^2-2x+2y\)

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

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

b) Ta có: \(x^2-4x+4-x^2y+2xy\)

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

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

c) Ta có: \(ax^2-3axy-x^2+6xy-9y^2\)

\(=ax\left(x-3y\right)-\left(x^2-6xy+9y^2\right)\)

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

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

d) Ta có: \(2a^2x-5a^2y-4x^2+30xy-25y^2\)

\(=a^2\left(2x-5y\right)-\left(4x^2-30xy+25y^2\right)\)

\(=a^2\left(2x-5y\right)-\left(2x-5y\right)^2\)

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

\(3x^3-4x^2+13x-4\)

\(=x^2\left(3x-1\right)-x\left(3x-1\right)+4\left(3x-1\right) \)

\(=\left(3x-1\right)\left(x^2-x+4\right)\)

a: \(ab+a+b+1\)

\(=a\left(b+1\right)+\left(b+1\right)\)

\(=\left(b+1\right)\left(a+1\right)\)

c: \(4x^2-12xy+3x-9y\)

\(=4x\left(x-3y\right)+3\left(x-3y\right)\)

\(=\left(x-3y\right)\left(4x+3\right)\)

2) \(x^4-5x^2+4\)

\(=x^4-x^2-4x^2+4\)

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

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

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

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

a,x²-4xy+4y²

=(x-2y²

b,4x⁴+9y²-12x²y

=(2x²)²+(3y)²-12x²y

(2x²-3y)

a) x² - 4xy + 4y²

= x² - 2.x.2y + (2y)²

=( x- y)²

b) 4x⁴ + 9y² -12x²y

= (2x²)² +12x²y + (3y)²

= [(2x2)  - 3y]

\(a,3x^3-6x^2+3x\)

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

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

\(b,16x^2y-4xy^2-4x^3\)

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

\(=-4x\left(x-2y+y\sqrt{3}\right)\left(x-2y-y\sqrt{3}\right)\)

1.A

2.C

3.B

4.C

a

c

b

c

(x-1)y^2-4(x-1)y