Question

Simplify the expression to a polynomial in standard form:

(4x^2+x-1)(-3x^2-3x-3)(4x2+x−1)(−3x2−3x−3)

Answer 1

`(144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2)`

Explanation:

To better understand the question we need to properly format the expression

`(4x^2+x-1)(-3x^2-3x-3)(4x^2+x-1)(-3x^2-3x-3)`

as we can see we have three brackets, we can proceed by first opening the first two brackets, we have.

`(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\`

we then continue by collecting like terms

`=-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)`

we then solve for the remaining two brackets

`(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\`

we then continue by collecting like terms

`=-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)`

from the two brackets we obtained
`(-12x^4-15x^3-12x^2+3)` each, we now have to multiply both terms together and solve we have

`(-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\\`

collecting and summing all like terms we have

`=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`