Question

phân tích đa thức sau thành nhân tử :

a.x^2 + x - y^2 +y

b.3x^2 + 3y^2 - 6xy - 12

Answer 1

a) x² +x -y² + y = ( x² -y² ) +(x+y)

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

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

b) 3x² +3y² -6xy -12 = 3(x² +y² - 2xy) -12

                                 =3 [ (x-y)² -4]

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

Answer 2

a) x² + x - y² + y

= (x² - y²) + (x + y)

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

= x + y

b) 3x² + 3y² - 6xy - 12

= 3 (x² + y² - 2xy - 4)

= 3 [(x² - 2xy + y²) - 4]

= 3 [(x - y)² - 2²]

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

(sai thì thôi)

Answer 3

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

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

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

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

\(3x^2+3y^2-6xy-12\)

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

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

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

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

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