Question

23. Simplifique estas expressões em seu caderno :

A) ( 2a+1 )³ - 6a(2a+1)
B) ( a - b )³ - 3ab( b- a )
C) ( x - 2y)³ + 6xy · ( x - 2y )

Answer 1

a)
$(2a+1)^3-6a(2a+1)=$

$[(2a)^3+3(2a)^2.1+3.2a.1^1+1^3]-12a^2-6a= \\ 8a^3+12a^2+6a+1-12a^2-6a= \\ 8a^3+1=$

fatorando
$8a^3+1=(3a+1)(9a^2+3a+1)$

b)
$(a-b)^3-3ab(b-a)= \\ a^3-3a^2b+3ab^2-b^3-3ab^2+3a^2b= \\ a^3-b^3$

fatorando
$a^3-b^3=(a-b)(a^2+ab+b}2)$


c)
$(x-2y)^3+6xy(x-2y)= \\ x^3-6x^2y+12xy^2-8y^3+6x^2y-12xy^2= \\ x^3-8y^3$

fatorando
$x^3-8y^3=(x-2y)(x^2+2xy+4y^2)$