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

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

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

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

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

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)

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) \(x^4-y^4\)

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

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

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

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) \(125x^3-1\)

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

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

\(a,=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\\ b,=\left(x+y\right)\left(x-5\right)\\ c,=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2y\right)\left(x-y\right)\\ d,=x^2-2xy=x\left(x-2y\right)\\ e,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

Bài 3: 

a: \(x^2-16=\left(x-4\right)\cdot\left(x+4\right)\)

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

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

a) x⁴ + 2x² + 1

= (x²)² + 2.x².1 + 1²

= (x² + 1)²

b) 4x² - 12xy + 9y²

= (2x)² - 2.2x.3y + (3y)²

= (2x - 3y)²

c) -x² - 2xy - y²

= -(x² + 2xy + y²)

= -(x + y)²

d) (x + y)² - 2(x + y) + 1

= (x + y)² - 2.(x + y).1 + 1²

= (x - y + 1)²

e) x³ - 3x² + 3x - 1

= x³ - 3.x².1 + 3.x.1² - 1³

= (x - 1)³

g) x³ + 6x² + 12x + 8

= x³ + 3.x².2 + 3.x.2² + 2³

= (x + 2)³

h) x³ + 1 - x² - x

= (x³ + 1) - (x² + x)

= (x + 1)(x² - x + 1) - x(x + 1)

= (x + 1)(x² - x + 1 - x)

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

k) (x + y)³ - x³ - y³

= (x + y)³ - (x³ + y³)

= (x + y)³ - (x + y)(x² - xy + y²)

= (x + y)[(x + y)² - x² + xy - y²]

= (x + y)(x² + 2xy + y² - x² + xy - y²)

= (x + y).3xy

= 3xy(x + y)