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

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

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

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

      \(2x^2-8y^2+5xy^2-10y^3\)

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

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

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

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

      \(3x^3-12x^2y+12-75xz^2\)

\(=3\left[x^3-4x^2y+4-25xz^2\right]\)

a: x^2+4xy-21y^2

\(=x^2+7xy-3xy-21y^2\)

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

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

b: \(5x^2+6xy+y^2\)

\(=5x^2+5xy+xy+y^2\)

=5x(x+y)+y(x+y)

=(x+y)(5x+y)

c: \(x^2+2xy-15y^2\)

\(=x^2+5xy-3xy-15y^2\)

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

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

d: \(x^2-7xy+10y^2\)

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

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

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

a) \(x^2+4xy-21y^2\)

\(=x^2+7xy-3xy-21y^2\)

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

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

b) \(5x^2+6xy+y^2\)

\(=5x^2+5xy+xy+y^2\)

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

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

c) \(x^2+2xy-15y^2\)

\(=x^2+5xy-3xy-15y^2\)

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

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

d) \(x^2-7xy+10y^2\)

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

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

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

a) x² + 4xy - 21y²

= x² - 3xy + 7xy - 21y²

= (x² - 3xy) + (7xy - 21y²)

= x(x - 3y) + 7y(x - 3y)

= (x - 3y)(x + 7y)

b) 5x² + 6xy + y²

= 5x² + 5xy + xy + y²

= (5x² + 5xy) + (xy + y²)

= 5x(x + y) + y(x + y)

= (x + y)(5x + y)

c) x² + 2xy - 15y²

= x² + 2xy + y² - 16y²

= (x² + 2xy + y²) - 16y²

= (x + y)² - (4y)²

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

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

d) x² - 7xy + 10y²

= x² - 2xy - 5xy + 10y²

= (x² - 2xy) - (5xy + 10y²)

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

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

\(2x^2y+4xy^2+2y^3-8\) 

\(=2y\left(x^2+2xy+y^2\right)-8\)

\(=2y\left(x+y\right)^2-8\) 

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

thank you huỳnh thanh phong

Đề sai nhé .Sửu lại

\(x^2-4x^2y^2+4+4x\)

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

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

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

1) \(3x^3-12x\)

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

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

2)\(x^3+x^2-x-1\)

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

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

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

3) \(x^2-7xy+10y^2\)

\(=\left(x^2-2xy\right)-\left(5xy-10y^2\right)\)

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

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

1) \(3x^3-12x\)

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

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

2) \(x^3+x^2-x-1\)

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

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

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

1)   \(3x^3-12x\)

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

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

2)     \(x^3+x^2-x-1\)

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

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

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

3)      \(x^2-7xy+10y^2\)

\(=\left(x^2-2xy\right)-\left(5xy-10y^2\right)\)

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

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