Respuesta :

64 is 4^3
x^12 is (x^4)^3
27 is 3^3
using the formula (a^3+b^3)=a^2-ab+b^2), we have
(4x^4+3y)(16x^8-12x^4y+9y^2)

Answer:  The complete factored form of the given expression is [tex](4x+3y)(16x^2-12xy+9y^2).[/tex]

Step-by-step explanation:  We are given to factor the following cubic expression completely :

[tex]E=64x^3+27y^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following formula :

[tex]a^3+b^3=(a+b)(a^2-ab+b^2).[/tex]

We have, from expression (i) that

[tex]E\\\\=64x^3+27y^3\\\\=(4x)^3+(3y)^3\\\\=(4x+3y)((4x)^2-4x\times3y+(3y)^2)\\\\=(4x+3y)(16x^2-12xy+9y^2).[/tex]

Thus, the complete factored form of the given expression is [tex](4x+3y)(16x^2-12xy+9y^2).[/tex]