Question

Descompuneti in factori,grupand mai intai convenabil termenii:
a)3x+3y+az+ay
b)7a+ab-7x-bx
c)2x+2y+abx+aby
d)5x^2+15x^2+4x+12
e)5ax^2+4ax^3+10a^2x+8a^2x^2
f)12x^2y^3+4x^2+9y^2z^2+3z^2
g)5xy+2x^2y+10x^2y^2+4x^3y^2
h)2x^2+3a^2x-4ax-6a^3

Answer 1

a)3x+3y+ax+ay =3(x+y)+a(x+y)=(x+y)(3+a)
b)7a+ab-7x-bx=a(7+b)-x(7+b)=(7+b)(a-x)
c)2x+2y+abx+aby=2(x+y)+ab(x+y)=(x+y)(2+ab)
d)5x^3+15x^2+4x+12=x(5x^2+4x)+3(5x^2+4)=(5x^2+4)(x+3)
e)5ax^2+4ax^3+10a^2x+8a^2x^2=ax^2(5+4x)+2a^2x(5+4x)=(5+4x)(ax^2+2a^2x)=
=ax(5+4x)(x+2a)
f)12x^2y^2+4x^2+9y^2z^2+3z^2=4x^2(3y^2+1)+3z^2(3y^2+1)=
=(3y^2+1)(4x^2+3z^2)
g)5xy+2x^2y+10x^2y^2+4x^3y^2=xy(5+2x)+2x^2y^2(5+2x)=
=(5+2x)(xy+2x^2y^2)=xy(5+2x)(1+2xy)
 h)2x^2+3a^2x-4ax-6a^3 =x(2x+3a^2)-2ax(2x+3a^2) =(2x+3a^2)(x-2ax) =
=x(2x+3a^2)(1-2a)

Answer 2

$a).3x+3y+ax+ay=3(x+y)+a(x+y)=(x+y)(3+a) \\ b).7a+ab-7x-bx=a(7+b)-x(7+b)=(7+b)(a-x) \\ c).2x+2y+abx+aby=2(x+y)+ab(x+y)=(x+y)(2+ab) \\ d).5x^3+15x^2+4x+12=5x^2(x+3)+4(x+3)=(x+3)(5x^2+4) \\ e).5ax^2+4ax^3+10a^2x+8a^2x^2=ax^2(5+4x)+2a^2x(5a+4x)= \\ =(5a+4x)(ax^2+2a^2x) \\ f).12x^2y^2+4x^2+9y^2z^2+3z^2=4x^2(3y^2+1)+3z^2(3y^2+1)= \\ =(3y^2+1)(4x^2+3z^2) \\ g).5xy+2x^2y+10x^2y^2+4x^3y^2=xy(5+2x)+2x^2y^2(5+2x)= \\ =(5+2x)(xy+2x^2y^2) \\ h).2x^2+3a^2x-4ax-6a^3=x(2x+3a^2)-2a(2x+3a^2)= \\ =(2x+3a^2)(x-2a)$