1: \(\left(x-y\right)^3+\left(x+y\right)^3-6xy^2\)

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

\(=2x^3\)

2: \(8x^3-36x^2y+54xy^2-28y^3\)

\(=8x^3-36x^2y+54xy^2-27y^3-y^3\)

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

3: \(x^3-3x^2+3x-2\)

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

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

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

Giải:

1) \(a^3-3a^2+3a-1\)

\(=a^3-3a^2.1+3a.1^2-1^3\)

\(=\left(a-1\right)^3\)

Vậy ...

2) \(x^3+6x^2+12x+8\)

\(=x^3+3.x^2.2+3.x.2^2+2^3\)

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

Vậy ...

3) \(8x^3-12x^2+6x-1\)

\(=\left(2x\right)^3-3.\left(2x\right)^2.1+3.2x.1^2-1^3\)

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

Vậy ...

4) \(x^3-6x^2y+12xy^2-8y^3\)

\(=x^3-3.x^2.2y+3.x.\left(2y\right)^2-\left(2y\right)^3\)

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

Vậy ...

nó dễ ợt mà -_- 

x²y²+4xy+4=(xy+2)² xong :)) 

 ( 3x+2). (3x-2)+(x-3)²-10x    

=9x²-4+x²-6x+9-10x

=9x²-4+x²-6x+9

=10x-16x+5

(2x+y)²+ (x-2y)²-5. (x+y).(x-y)

=4x²+4xy+y²+x²-4xy+4y²-5.(x²-y²)

=4x²+4xy+y²+x²-4xy+4y²-5x²+5y²

=10y²

(3x-5)²- x.(3x-5)

=9x²-30x+25-3x²+15

=6x²-30x+40

mjk làm ruj đó đúng mjk đi

Rút gọn biểu thức

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

đề sai rùi phải là : \(36\left(x-y\right)^2-25\left(2x-1\right)^2\)

\(=>\left[6\left(x-y\right)\right]^2-\left[5\left(2x-1\right)\right]^2=\left[6\left(x-y\right)-5\left(2x-1\right)\right]\left[6\left(x-y\right)+5\left(2x-1\right)\right]\)

\(=>\left(6x-6y-10x+5\right)\left(6x-6y+10x-5\right)=\left(5-4x-6y\right)\left(16x-6y-5\right)\)

Áp dụng HDT : x^2 -y^2 =(x-y) (x+y)

Ủng hộ = 1 cái t i c k nha cảm ơn

\(B=\left(\dfrac{1}{2}x-1\right)^3=\left(-1-1\right)^3=\left(-2\right)^3=-8\)

\(C=\left(x+1\right)^3-1000\)

\(=100^3-1000=999000\)

\(D=27x^3+54x^2+36x+8-4\)

\(=\left(3x+2\right)^3-4=\left(-6+2\right)^3-4\)

\(=-64-4=-68\)

a: \(25x^2-\dfrac{10}{3}xy+\dfrac{1}{9}y^2=\left(5x-\dfrac{1}{3}y\right)^2\)

b: \(25x^2-15x+\dfrac{9}{4}=\left(5x-\dfrac{3}{2}\right)^2\)

c: \(\left(2x+\dfrac{1}{2}y\right)\left(4x^2-xy+\dfrac{1}{4}y^2\right)=8x^3+\dfrac{1}{8}y^3\)

d: \(\left(x^2-\dfrac{2}{3}\right)\left(x^4+\dfrac{2}{3}x^2+\dfrac{4}{9}\right)=x^6-\dfrac{8}{27}\)