`N=(3x-1)^2-2(9x^2-1)+(3x+1)^2

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

`=(3x-1-3x-1)^2=(-2)^2=4`

`x^3-6x^2y+12xy^2-8y^3`

`=x^3-3.x^2 .2y +3.x.(2y)^2-(2y)^3`

`=(x-2y)^3`

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

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

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

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

a.\(27x^3+27x^2+9x+1=\left(3x+1\right)^3\)

b.\(x^3-6x^2+12x-8=\left(x-2\right)^3\)

c.\(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

a)\(69^2-31^2=\left(69-31\right)\left(69+31\right)=38.100=3800\)

\(1023^2-23^2=\left(1023-23\right)\left(1023+23\right)=1000.1046=1046000\)

a.\(x^3-8=x^3-2^3=\left(x-2\right)\left(x^2+2x+4\right)\)

b.\(27x^3+125y^3=\left(3x\right)^3+\left(5y\right)^3=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)

c.\(\left(2x-1\right)^3+8=\left(2x-1\right)^3+2^3=\left(2x+1\right)\left[\left(2x-1\right)^2-2\left(2x-1\right)+4\right]\)

d.\(x^6+6^3=\left(x^2+6\right)\left(x^4-6x+36\right)\)

e.\(1-27x^3=1-\left(3x\right)^3=\left(1-3x\right)\left(1+3x+9x^2\right)\)

j.\(\left(x-3\right)^3-27=\left(x-3\right)^3-3^3=\left(x-6\right)\left[\left(x-3\right)^2+3\left(x-3\right)+9\right]\)

g.\(x^3y^3+125=\left(xy\right)^3+5^3=\left(xy+5\right)\left(x^2y^2-5xy+25\right)\)

t.\(8x^3-\frac{1}{8}=\left(2x\right)^3-\left(\frac{1}{2}\right)^3=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)

u.\(x^3+\frac{1}{27}=x^3+\left(\frac{1}{3}\right)^3=\left(x+\frac{1}{3}\right)\left(x^2-\frac{x}{3}+\frac{1}{9}\right)\)

a)\(6x-9-x^2\)

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

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

b)\(x^2+4y^2+4xy\)

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

c)\(x^2+8x+16\)

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

d)\(9x^2-12xy+4y^2\)

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

e)\(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

f)\(4x^2-4x+1\)

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

j)\(x^2+6x+9\)

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

h)\(9x^2-6x+1\)

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

#H

a, 6x - 9 - x² = - x² + 6x - 9 = - (x² - 6x + 9) = - (x - 3)²

b, x² + 4y² + 4xy = x² + 2. x . 2y + (2y)² = (x + 2y)²

c, x² + 8x + 16 = x² + 2 . x . 4 + 4² = (x + 4)²

d, 9x² - 12xy + 4y² = (3x)² - 2 . 3x . 2y + (2y)² = (3x - 2y)²

e, - 25x²y² + 10xy - 1 = - (25x²y² - 10xy + 1) = - [(5xy)² - 2 . 5xy + 1] = - (5xy - 1)²

f, 4x² - 4x + 1 = (2x)² - 2 . 2x + 1 = (2x - 1)²

j, x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

h, 9x² - 6x + 1 = (3x)² - 2 . 3x + 1 = (3x - 1)²

uuuttyutyyuyuyyuyuyuyuyuyuyuy