a, 2xy^2 ( x^3 -3xy - 4 )

b, x^2 - 4x - 4x +16

= x(x-4) - 4(x-4)

= (x-4) (x-4)

Lời giải:

a.

$2x^4y^2-6x^2y^3-8xy^2=2xy^2(x^3-3xy-4)$

b. 

$x^2-8x+16=x^2-2.4.x+4^2=(x-4)^2$

c.

$12x^2-12=12(x^2-1)=12(x-1)(x+1)$

d. 

$5x^2y-20xy+20y=5y(x^2-4x+4)=5y(x-2)^2$
e.

$3x^2y^2-27y^2=3y^2(x^2-9)=3y^2(x-3)(x+3)$

f. 

$8x^3-27y^3=(2x)^3-(3y)^3=(2x-3y)(4x^2+6xy+9y^2)$

g.

$4x^4-8x^3+4x^2=(2x^2)^2-2.2x^2.2x+(2x)^2$

$=(2x^2-2x)^2=[2x(x-1)]^2=4x^2(x-1)^2$
h.

$7x^2y^2-28y^4=7y^2(x^2-4y^2)=7y^2(x-2y)(x+2y)$

$

a) Ta có: \(1+6x-6x^2-x^3\)

\(=\left(1-x\right)\left(x^2+x+1\right)+6x\left(1-x\right)\)

\(=\left(1-x\right)\left(x^2+7x+1\right)\)

b:Ta có: \(x^3-4x^2+8x-8\)

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

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

c: Ta có: \(x^3+2x^2+2x+1\)

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

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

d: Ta có: \(8x^3-12x^2+6x-1\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)

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

Ta có:  3 x 2 + 2 x + 4 = 8 x 3 + 12 x 2 + 8 x + 1 3 x 2 + 2 x + 5 = ( 2 x + 1 ) 3 + 2 x + 1 3 x 2 + 2 x + 5  (1)

Dễ thấy  3 x 2 + 2 x + 4 > 0  với mọi x. Đặt  u = 3 x 2 + 2 x + 4 v = 2 x + 1 .

 Ta có:   ( 1 ) ⇔ u = v 3 + v u 2 + 1 ⇔ u 3 + u = v 3 + v ⇔ ( u − v ) ( u 2 + u v + v 2 + 1 ) = 0 ⇔ u = v

(Vì  u 2 + u v + v 2 + 1 = u + v 2 2 + 3 4 v 2 + 1 > 0 )

  u = v ⇔ 3 x 2 + 2 x + 4 = 2 x + 1 ⇒ 3 x 2 + 2 x + 4 = 4 x 2 + 4 x + 1 x 2 − 2 x − 3 = 0 ⇒ x = 3   h o a c   x = − 1.

Thử lại, ta nhận x= 3

\(=8x^3+27-8x^3-7=20\)

bằng 20

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

\(8x^3+12x^2+6x+1=0\)

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

\(\Leftrightarrow\left(2x+1\right)^3=0\)

\(\Leftrightarrow2x+1=0\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

đề sai, mk sửa :

\(8x^3+12x^2+6x+1=0\)

\(\Leftrightarrow\left(2x+1\right)^3=0\)

\(\Leftrightarrow2x+1=0\)

\(\Leftrightarrow2x=-1\)

\(\Leftrightarrow x=\dfrac{-1}{2}\)

Vậy ...

1: Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)

\(=x^3+27-x^3-54\)

=-27

2: Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=2y^3\)​

\(1,=x^3+270-x^3-54=-27\\ 2,=8x^3+y^3-8x^3+y^3=2y^3\\ 3,=x^3-3x^2+3x-1-x^3-8+3x^2-48=3x-57\\ 4,=x^3-x-x^3-1=-x-1\\ 5,=8x^3-5\left(8x^3+1\right)=-32x^3-5\\ 6,=27+x^3-27=x^3\\ 7,làm.ở.câu.3\\ 8,=x^3-6x^2+12x-8+6x^2-12x+6-x^3-1+3x\\ =3x-3\)

a: A=(2x-1)^3

Khi x=5,5 thì A=(2*5,5-1)^3=10^3=1000

b: B=27x^3+54x^2+36x+7

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

=(3x+2)^3-1

=(-8+2)^3-1

=(-6)^3-1=-217