Question

Phân tích da thức thành nhân tử :

a ) 6a^2y - 3aby +4a^2x - 2abx

b ) ax -bx -2cx -2a +2b +4c

c ) x^9 +1

d ) 25x^2 - 20xy +4y^2

e )x^2 +2xy +y^2 - 25

 

Answer 1

a ) \(6a^2y-3aby+4a^2x-2abx\)

\(=3ay\left(2a-b\right)+2ax\left(2a-b\right)\)

\(=\left(3ay+2ax\right)\left(2a-b\right)\)

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

b ) \(ax-bx-2cx-2a+2b+4c\)

\(=a\left(x-2\right)-b\left(x-2\right)-2c\left(x-2\right)\)

\(=\left(a-b-2c\right)\left(x-2\right)\)

c ) \(x^9+1\)

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

\(=\left(x^3+1\right)\left(x^6-x^2+1\right)\)

\(=\left(x+1\right)\left(x^2-x+1\right)\left(x^6-x^3+1\right)\)

d ) \(25x^2-20xy+4y^2\)

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

e ) \(x^2+2xy+y^2-25\)

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

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