a) \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

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

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

\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)

b) \(3x^4y^2+3x^3y^2+3xy^2+3y^2\)

\(=\left(3x^4y^2+3xy^2\right)+\left(3x^3y^2+3y^2\right)\)

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

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

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

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

c) \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)

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

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

a, \(=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)

b, \(\left(x+y-x+y\right)[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2]\)

\(=2y[x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2]\)

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

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

câu a, b áp dụng hằng đẳng thức rồi làm nha 

c) 3x⁴y² + 3x³y² + 3xy² + 3y²

= ( 3x⁴y² + 3x³y² ) + ( 3xy² + 3y² )

= 3x³y² ( x + 1) + 3y² ( x + 1 )

= ( 3x³y² + 3y² ) ( x + 1 )

= 3y² ( x³ + 1 ) ( x + 1 )

= 3y² ( x + 1 ) ( x² - x + 1 ) ( x + 1 )

= 3y² ( x + 1 )² ( x² - x + 1 )

a) (xy +1)²- (x-y)²

=(xy +1-x+y)(xy+1+x-y)

b) (x + y)³ - (x - y)³

= (x+y-x+y)((x+y)²+(x+y)(x-y)+(x - y)²)

= 2y(x²+2xy+y²+x²+xy-xy-y²+x²-2xy+y²)

=2y(3x²+y²)

c) 3x⁴y² + 3x³y² + 3xy² + 3y²

=3y²(x⁴+x³+x+1)

= 3y²(x³(x+1)+(x+1)

= 3y²(x+1)(x³+1)

ko bt đúng ko

Bài 2: 

a: \(3x^2-3xy=3x\left(x-y\right)\)

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

c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)

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

ỳtct7ct7c7c7t79tc9

a: =(6x)^2-(3x-2)^2

=(6x-3x+2)(6x+3x-2)

=(9x-2)(3x+2)

d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)

\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)

=8x(x^2+1)

e: =(4x)^2-2*4x*3y+(3y)^2

=(4x-3y)^2

f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)

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

g: =(4x)^3+1^3

=(4x+1)(16x^2-4x+1)

k: =x^3(27x^3-8)

=x^3(3x-2)(9x^2+6x+4)

l: =(x^3-y^3)(x^3+y^3)

=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)

a: =(a^2-b^2)-(2a-2b)

=(a-b)(a+b)-2(a-b)

=(a-b)(a+b-2)

b: =(3x-3y)+5y(x-y)

=3(x-y)+5y(x-y)

=(x-y)(5y+3)

c: \(=\left(x+y\right)^2\left(x-y\right)+x\left(y-x\right)\)

=(x-y)*(x+y)^2-x(x-y)

=(x-y)[(x+y)^2-x]

d: \(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)

=(-x-4y+5)(3x+2y+3)

e: =16-(x^2-4xy+4y^2)

=16-(x-2y)^2

=(4-x+2y)(4+x-2y)

g: =9x^2-6x+1-(3xy-y)

=(3x-1)^2-y(3x-1)

=(3x-1)(3x-y-1)

h: =(x-y)^3-z^3

=(x-y-z)[(x-y)^2+z(x-y)+z^2]

=(x-y-z)(x^2-2xy+y^2+xz-yz+z^2)

a) \(a^2-b^2-2a+2b\)

\(=\left(a^2-b^2\right)-\left(2a-2b\right)\)

\(=\left(a+b\right)\left(a-b\right)-2\left(a-b\right)\)

\(=\left(a-b\right)\left(a+b-2\right)\)

b) \(3x-3y-5x\left(y-x\right)\)

\(=\left(3x-3y\right)+5x\left(x-y\right)\)

\(=3\left(x-y\right)+5x\left(x-y\right)\)

\(=\left(5x+3\right)\left(x-y\right)\)

c) \(x\left(x+y\right)^2-y\left(x+y\right)^2+xy-x^2\)

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

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

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

d) \(\left(x-y+4\right)^2-\left(2x+3y-1\right)\)

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

\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)

b: \(x^2-6x+xy-6y\)

\(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

c: \(2x^2+2xy-x-y\)

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

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

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

\(x^2+3x-10\)

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

\(=x\left(x-2\right)-5\left(x-2\right)\)

\(=\left(x-2\right)\left(x-5\right)\)

hk tốt

^^

a) \(x^4-y^4\)

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

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

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

b) \(x^2-3y^2\)

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

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

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

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

\(=\left(5x-5y\right)\left(x+y\right)\)

\(=5\left(x-y\right)\left(x+y\right)\)

d) \(9\left(x-y\right)^2-4\left(x+y\right)^2\)

\(=\left[3\left(x-y\right)+2\left(x+y\right)\right]\left[3\left(x-y\right)-2\left(x+y\right)\right]\)

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

\(=\left(5x-y\right)\left(x-5y\right)\)

e) \(\left(4x^2-4x+1\right)-\left(x+1\right)^2\)

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

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

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

f) \(x^3+27\)

\(=x^3+3^3\)

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

g) \(27x^3-0,001\)

\(=\left(3x\right)^3-\left(0,1\right)^3\)

\(=\left(3x-0,1\right)\left(9x^2+0,3x+0,01\right)\)

h) \(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

1) 3a - 3b + a^2 - ab

= 3(a - b) + a(a - b)

= (a - b)(a + 3)

2) = 3xy(x^2 + y^2)/(x^2 + y^2) = 3xy