a)\(A=3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-z\right)\left(x+y+z\right)\)b) \(A=\left(x+y\right)^2-2\left(x+y\right)+1=\left(x+y-1\right)^2\)

c) \(A=x^2+y^2+2xy+yz+zx=\left(x+y\right)^2+z\left(x+y\right)=\left(x+y\right)\left(x+y+z\right)\)

 \(a,4x^2-1\)

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

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

\(b,25x^2-0,09\)

\(=\left(5x\right)^2-\left(0,3\right)^2\)

\(=\left(5x-0,3\right)\left(5x+0,3\right)\)

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

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

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

\(e,9-\left(x-y\right)^2\)

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

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

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

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

\(f,\left(x^2+4\right)^2-16x^2\)

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

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

\(=\left(x^2-2\cdot x\cdot2+2^2\right)\left(x^2+2\cdot x\cdot2+2^2\right)\)

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

#\(Toru\)

`#3107`

a)

`4x^2 - 1`

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

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

b)

`25x^2 - 0,09`

`= (5x)^2 - (0,3)^2`

`= (5x - 0,3)(5x + 0,3)`

d)

`(x - y)^2 - 4`

`= (x - y)^2 - 2^2`

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

e)

`9 - (x - y)^2`

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

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

f)

`(x^2 + 4)^2 - 16x^2`

`= (x^2 + 4)^2 - (4x)^2`

`= (x^2 - 4x + 4)(x^2 + 4x + 4)`

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

_____

Tất cả các câu trên bạn sử dụng hđt:

`A^2 - B^2 = (A - B)(A + B)`

\(#MaiChangLaAnhDau..\)

tách nhỏ câu hỏi ra bạn dài quá

help

Rối ghê

\(14x^2y-21xy^2+28x^2y=7xy\left(2x-3y+4x\right)=21xy\left(2x-y\right)\)

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

\(10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)

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

a: \(\left(x-3\right)^2-\left(2x-5\right)^2\)

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

\(=\left(2-x\right)\left(3x-8\right)\)

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

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

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

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

\(a,=x\left(4x^2-1\right)=x\left(2x-1\right)\left(2x+1\right)\\ b,=2\left(3x-2\right)-x\left(3x-2\right)=\left(2-x\right)\left(3x-2\right)\\ c,=x\left(y-1\right)-\left(y-1\right)=\left(x-1\right)\left(y-1\right)\\ d,=\left(y+2\right)^2-4x^2=\left(y+2-2x\right)\left(y+2+2x\right)\\ e,=x^2-x-2x+2=\left(x-1\right)\left(x-2\right)\)

a) \(4x^3-x^2=x^2\left(4x-1\right)\)

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

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

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

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

a) 3x(x + 1) - 5y(x + 1)

= (x + 1)(3x - 5y)

b) 3x(x - 6) - 2(x - 6)

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

c) 4y(x - 1) - (1 - x)

= 4y(x - 1) + (x - 1)

= (x - 1)(4y + 1)

d) (x - 3)³ + 3 - x

= (x - 3)³ - (x - 3)

= (x - 3)[(x - 3)² - 1]

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

= (x - 3)(x - 4)(x - 2)

e) 7x(x - y) - (y - x)

= 7x(x - y) + (x - y)

= (x - y)(7x + 1)

h) 3x³(2y - 3z) - 15x(2y - 3z)²

= (2y - 3z)[3x³ - 15x(2y - 3x)]

= 3x(2y - 3x)[x² - 5(2y - 3x)]

= 3x(2y - 3x)(x² - 10y + 3x)

= 3x(2y - 3x)(x² + 3x - 10y)

k) 3x(x + 2) + 5(-x - 2)

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

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

l) 18x²(3 + x) + 3(x + 3)

= (x + 3)(18x² + 3)

= 3(x + 3)(6x² + 1)

m) 7x(x - y) - (y - x)

= 7x(x - y) + (x - y)

= (x - y)(7x + 1)

n) 10x(x - y) - 8y(y - x)

= 10x(x - y) + 8y(x - y)

= (x - y)(10x + 8y)

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

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) \(125x^3-1\)

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

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

tách nhỏ câu hỏi ra

a,=5xy(x-2y)

b,=3(x+3)+(x-3)(x+3)

=(x+3)+x

c=xy(x-y)+z(x-y)

  =(x-y)(xy+z)

d=7xy(2x-3y+4xy)

e,=x(x+y)-5(x+y)

  =  (x+y)(x-5)

f, =10x(x-y)+8(x-y)

   =(x-y)(10x+8)

g,=(3x+1-x+1)(3x+1+x+1)

=2x(4x+2)

h,=x^2-3x-2x+6

   = x(x-3)-2(x-3)

   =(x-3)(x-2)

\(a,=5\left(x-2y\right)\\ b,=3xy\left(x-2y\right)\\ c,=\left(x-y\right)\left(x+3\right)\\ d,=\left(x-1\right)\left(2x-4x^2\right)=2x\left(1-2x\right)\left(x-1\right)\\ e,=\left(x-2y\right)^2\\ f,=\left(3x-4y\right)\left(3x+4y\right)\\ g,=\left(x-3\right)\left(x^2+3x+9\right)\)

a. 5x - 10y 

= 5(x - 2y)

b. 3x²y - 6xy²

= 3xy(x - 2y)

c. x(x - y) - 3(y - x)

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

= (x + 3)(x - y)

d. 2x(x - 1) + 4x²(1 - x)

= 2x(x - 1) - 4x²(x - 1)

= (2x - 4x²)(x - 1)

= 2x(1 - 2x)(x - 1)

e. x² - 4xy + 4y²

= (x - 2y)²

f. 9x² - 16y²

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

g. x³ - 27

= (x - 3)(x² + 3x + 9)