Question

1) Descompuneti in produs de factori:

a) a^2 x^3 + 3a^2 x^2 +ax^2 + 3ax

b) 2a^2 x + 3ax - 2a^3 -3a^2

c) x^3 y - 4xy^3 + 16x^2 y^3 - 4x^4 y

Dau COROANA!

Answer 1

a)

a²x³ + 3 a²x² + a x² + 3 ax =  a x ( a x + 1 ) ( x + 3 )

= a x ( a x²  + 3 a x + x + 3 ) =

=  a x [  x ( a x + 1 ) + 3 ( a x + 1 ) ] =

=  a x ( a x + 1 ) ( x + 3 )  

__________________________

b)

2 a² x + 3 a x - 2 a³ - 3 a² = a ( x - a ) ( 2 a + 3 )

= 2 a² ( x - a ) + 3 a ( x - a ) =

= ( x - a ) ( 2 a² + 3 a ) =

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

______________________________

c)

x³y - 4 x y³ + 16 x² y³ - 4 x⁴ y =x y ( 1 - 4 x ) ( x - 2 y ) ( x + 2 y )

= x y ( x² - 4 y² + 16 x y² - 4 x³ ) =

= x y [ x² ( 1 - 4 x ) - 4 y² ( 1 - 4 x ) ] =

= x y ( 1 - 4 x ) ( x² - 4 y²) =

= x y ( 1 - 4 x ) ( x - 2 y) ( x + 2 y )