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

b11 (4n+3)^2-25

=(4n+3-25)(4n+3+25)

=(4n-22)(4n+28)

b12

(2n+3)^2-9=(2n+3-3)(2n+3+3)=2n2(n+3)=4n(n+3) chia ht cho 4

\(A=\frac{1}{x^2-3x}+\frac{1}{x\left(x+3\right)}+\frac{1}{x^2-9}\)ĐK : \(x\ne0;-3;3\)

\(=\frac{1}{x\left(x-3\right)}+\frac{1}{x\left(x+3\right)}+\frac{1}{x^2-9}=\frac{x+3+x-3+x}{x\left(x-3\right)\left(x+3\right)}\)

\(=\frac{3x}{x\left(x-3\right)\left(x+3\right)}=\frac{3}{\left(x-3\right)\left(x+3\right)}\)

Thay x = 12 vào ta được : \(\frac{3}{\left(12-3\right)\left(12+3\right)}=\frac{3}{144-9}=\frac{3}{135}=\frac{1}{45}\)