Bài 1:

\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)

Bài 3:

\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)

Bài 1;

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

2) \(6x^2+12xy+6y^2=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)

3) \(2y^3+8y^3+8y=10y^3+8y=2y\left(5y^2+4\right)\)

4) \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

1) \(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

2) \(8x^2y-18y=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\)

3) \(24x^3-3=3\left(8x^3-1\right)=3\left(2x-1\right)\left(4x^2+2x+1\right)\)

Bài 3:

1) \(5x^2+10x+5-5y^2=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y\right]=5\left(x-y+1\right)\left(x+y+1\right)\)

2) \(3x^3-6x^2+3x-12xy^2=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=3x\left(x-2y-1\right)\left(x+2y-1\right)\)

3) \(a^3b-ab^3+a^2+2ab+b^2=ab\left(a^2-b^2\right)+\left(a+b\right)^2=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2=\left(a+b\right)\left(a^2b-ab^2+a+b\right)\)

4) \(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2-4x+4y\right)=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]=2x\left(x-y\right)\left(x+y-4\right)\)

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)

\(=2+\sqrt{3}+\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right)\left(\sqrt{2}+1\right)\)

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)

\(x^6-x^4+2x^3+2x\)

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

p/s: chúc bạn học tốt

\(x^6-x^4+2x^3+2x\)

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

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

(x-3)³ + 3 -x =0

=>x³-9x²+26x-24=0

=>x³-7x²+12x-2x²+14x-24=0

=>x(x²-7x+12)-2(x²-7x+12)=0

=>(x-2)(x²-7x+12)=0

=>(x-2)[x²-4x-3x+12]=0

=>(x-2)[x(x-4)-3(x-4)]=0

=>(x-2)(x-3)(x-4)=0

=>x-2=0 hoặc x-3=0 hoặc x-4=0

=>x=2 hoặc 3 hoặc 4

Vậy tập nghiệm của pt là S={2;3;4}

= (x-3)³ - (x-3) =0

(x-3)((x-3)² -1)=0

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

(x-3)(x-2)(x-4) =0

x = 3;2;4

đơn giản,dễ hiểu, vận dụng hđt đáng nhớ, có ai giỏi =em k

\(x^2-2xy+y^2-16\)

\(=\left(x-y\right)^2-16\)

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

p/s: chúc bạn học tốt

\(x^2-2xy+y^2-16\)

\(\Rightarrow\left(x-y\right)^2-16\)

\(\Rightarrow\left(x-y-4\right)\left(x-y+4\right)\)

Code : Breacker

1)x^2+x+2013x+2013=x(x+1)+2013(x+1)=(x+1)(x+2013)