Answer:
[tex](144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2)[/tex]
Step-by-step explanation:
To better understand the question we need to properly format the expression
[tex](4x^2+x-1)(-3x^2-3x-3)(4x^2+x-1)(-3x^2-3x-3)[/tex]
as we can see we have three brackets, we can proceed by first opening the first two brackets, we have.
[tex](4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\[/tex]
we then continue by collecting like terms
[tex]=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)[/tex]
we then solve for the remaining two brackets
[tex](4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\[/tex]
we then continue by collecting like terms
[tex]=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)[/tex]
from the two brackets we obtained[tex](-12x^4-15x^3-12x^2+3)[/tex] each, we now have to multiply both terms together and solve we have
[tex](-12x^4-15x^3-12x^2+3)(-12x^4-15x^3-12x^2+3)\\=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\[/tex]
collecting and summing all like terms we have
[tex]=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\=144x^8+180x^7+180x^7+144x^6+255x^6+180x^5+180x^5-36x^4+144x^4-36x^4-45x^3-45x^3-36x^2-36x^2\\\\\=144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2[/tex]
