27x³ - 27x² + 3x - 1 

= (3x)³ - 3.(3x)².1 + 3x.1² - 1 

= (3x - 1)³ 

ui sai hđt kìa b =))

(x+1)(x+2)(x+3)(x+4)-24

= (x^2 + 5x + 4)(x^2 + 5x + 6) - 24

đặt x^2 + 5x + 5 = a

ta có : (a - 1)(a + 1) - 24 = a^2 - 1 - 24

= a^2 - 25

= (a - 5)(a+5)

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

= (x^2 + 5x)(x^2 + 5x + 10)

= x(x + 5)(x^2 + 5x + 10)

x(x+1)(x+2)(x+3)+1

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

đặt x^2 + 3x + 1 = a

ta có : (a - 1)(a+1) + 1 = a^2 - 1 + 1 = a^2

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

$\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24$

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

$=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24$

Đặt $t=x^2+5x+4$ , ta có
$t\left(t+2\right)-24$

$=t^2+2t-24$

$=\left(t^2+2t+1\right)-25$

$={\left(t+1\right)}^2-5^2$

$=\left(t+1-5\right)\left(t+1+5\right)$

$=\left(t-4\right)\left(t+6\right)$

$=\left(x^2+5x+4-4\right)\left(x^2+5x+4+6\right)$

$=\left(x^2+5x\right)\left(x^2+5x+10\right)$

$x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1$

$=\left[x\left(x+3\right)\right]\left[\left(x+1\right)\left(x+2\right)\right]+1$

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

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

Đặt $x^2+3x=t\Rightarrow x^2+3x+2=t+2$

Do đó $\left(1\right)=t\left(t+2\right)+1=t^2+2t+1={\left(t+1\right)}^2$(*)

Vì $t=x^2+3x$ nên

$\left(\text{*}\right)={\left(x^2+3x+1\right)}^2$

 (2x⁴-8x²+8) : (4-2x²)

=  2(x⁴-4x²+4) : 2(2-x²)

= (x⁴-4x²+4) : (2-x²)

= (x²  - 2) : (2-x²)

=   - 1

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

\(\left(4-2x^2\right)=2\left(2-x^2\right)\Rightarrow\frac{2x^4+8x^2+8}{4-2x^2}=\frac{2\left(x^2+2\right)^2}{2\left(2-x^2\right)}=\frac{\left(x^2+2\right)^2}{2-x^2}\)

Nếu không sai đề thì tự phân tích rồi thực hiện phép chia đa thức

 a^2-2ab+1+2b-2a-3b^2  =  a^2 -2a . b+1 +2b-2a-3b^2 = -(b+a-1)(3b-a+1)

nha bạn chúc bạn học tốt 

cảm ơn bạn ♡•꧁༺༒✰ŞŦΔŘ✰༒༺꧁•♡✿(➻❥𝒢𝑜𝓁𝒹❃𝒮𝓉𝒶𝓇✤) ❀ nha  

a, x^3 + y^3  = (x + y)(x^2 - xy + y^2) = (x + y)[(x+y)^2 - 3xy]

mà x + y = 1 và xy = -1

=> x^3 + y^3 = 1(1^2 - 3(-1)) = 4

b, x^3 - y^3 = (x - y)(x^2 + xy + y^2) = (x-y)[(x-y)^2+3xy]

có x - y = 1 và xy = 6

=> 1(1^2 + 3.6) = 19

a)

\(27x^3-27x^2+3x+1\)

\(=\left(3x-1\right)\left(9x^2-6x-1\right)\)

HT :))

...

\(7.a,8x^6-12x^4+6x^2-1=\left(2x^2-1\right)\)

\(b,8\left(\frac{x}{2}+y\right)^3-6\left(x+2\right)^2x+12\left(x+2y\right)x^2-8x^3=\left[2\left(\frac{2y+x}{2}\right)-2x\right]^3=\left(2y-x\right)^3\)

\(c,\left(x-y\right)^3-\frac{3\left(x-y\right)^2}{2}y+\frac{3\left(x-y\right)}{4}y^2-\frac{y^3}{8}=\left(x-y-\frac{y}{2}\right)^3=\left(x-\frac{3}{2}y\right)^3\)

\(8.A=\left(x-y\right)^3+3xy\left(x-y\right)=x^3-3xy\left(x-y\right)+y^3+3xy\left(x-y\right)=x^3+y^3\)

\(B=\left(x+y\right)^3+3\left(x-y\right)\left(x+y\right)^2+3\left(x-y\right)^2\left(x+y\right)+\left(x-y\right)^3=\left(x+y+x-y\right)^3=8x^3\)

a, (25-15)(25+15)= 400

b, (205-95)(205+95)=33000

c,(36-14)(36+14)=1100

d, (950-850)(950+850)=180000

e, (1.24-0.24)^2=1

e, 1,24² - 2,48 x 0,24 + 0,24²

= 1,24²  - 2 x 1,24 x 0,24 + 0,24²

=   (1,24-0,24)²

=>  x+2=0         hoặc        x-1=0

       x=-2                            x=1

vậy...

𝑥(𝑥−1)+2(𝑥−1)=0

𝑥2−𝑥+2(𝑥−1)=0

𝑥2−𝑥+2𝑥−2=0

𝑥2+1𝑥−2=0

𝑥2+𝑥−2=0

𝑥=1

x=1x=1

𝑥=−2

học tút nhớ k nhé