Câu 1:

\(a^2+2ab+b^2-ac-bc\)

\(=\left(a+b\right)^2-c\left(a+b\right)\)

\(=\left(a+b\right)\left(a+b-c\right)\)

Câu 2:

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

\(=5\left(x-y\right)\left(x+y\right)-10\left(x-y\right)\)

\(=\left(x-y\right)\left(5x+5y-10\right)\)

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

Câu 3:

\(3x^2-6xy+3y^2-12z^2\)

\(=3\left[\left(x-y\right)^2-4z^2\right]\)

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

Câu 4:

\(x^4+x^3+x^2-1\)

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

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

Câu 5:

\(x^3-3x^2+3x-1-y^3\)

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

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

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

Câu 6:

\(x^4-x^2+2x-1\)

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

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

Câu 7:

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

\(=\left(x+y\right)^3-\left[\left(x+y\right)^3-3xy\left(x+y\right)\right]\)

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

moi hok lop 6 

=x^4(x-2)+2x^2(x-2)-3(x-2)

=(x-2)(x^4+2x^2-3)

Ta có:

$10x^2-x-11=0$

$\Delta=(-1)^2-4\cdot10\cdot(-11)=441=21^2$

$x=\dfrac{1\pm21}{20}$

$x=1$ hoặc $x=-\dfrac{11}{10}$

Vậy $x\in\left{1,-\dfrac{11}{10}\right}$.

$2x^2-3x-2=0$

$\Delta=(-3)^2-4\cdot2\cdot(-2)=25=5^2$

$x=\dfrac{3\pm5}{4}$

$x=2$ hoặc $x=-\dfrac12$

Vậy $x\in\left{2,-\dfrac12\right}$.

$2x^2-8=0$

$2(x^2-4)=0$

$(x-2)(x+2)=0$

$x=2$ hoặc $x=-2$

Vậy $x=\pm2$.

$3x^2-5x=0$

$x(3x-5)=0$

$x=0$ hoặc $x=\dfrac53$

Vậy $x\in\left{0,\dfrac53\right}$.

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

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

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

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

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

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

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

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

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

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

đề câu 2 thiếu kìa