Question

Fatore as expressões seguintes
a) 6x⁴y²z+8x³yz-12xy³z²
b) (2x+3y).a+5.(2x+3y)
c) 24ab²c²-36a²bc²+60a²b²c-12abc

Answer 1

a)   $6x^{4}y^{2}z+8x^{3}yz-12xy^{3}z^{2}=$

  $=2(3x^{4}y^{2}z+4x^{3}yz-6xy^{3}z^{2})=$

  $=2x(3x^{3}y^{2}z+4x^{2}yz-6y^{3}z^{2})=$

  $=2xy(3x^{3}yz+4x^{2}z-6y^{2}z^{2})=$

  $=2xyz(3x^{3}y+4x^{2}-6y^{2}z)$

b)   $(2x+3y)a+5(2x+3y)=$

  $=(2x+3y)(a+5)=$

  $=2ax+10x+3ay+15y=$

  $=2ax+3ay+10x+15y$

c)   $24ab^{2}c^{2}-36a^{2}bc^{2}+60a^{2}b^{2}c-12abc=$

  $=12(2ab^{2}c^{2}-3a^{2}bc^{2}+5a^{2}b^{2}c-abc)=$

  $=12a(2b^{2}c^{2}-3abc^{2}+5ab^{2}c-bc)=$

  $=12ab(2bc^{2}-3ac^{2}+5abc-c)=$

  $=12abc(2bc-3ac+5ab-1)$