Answer:
[tex]\textsf{B.} \quad 2+x-31x^2-57x^3-27x^4[/tex]
Step-by-step explanation:
Given expression:
[tex](1+4x+3x^2)(2-7x-9x^2)[/tex]
Use the distributive law and separate the first polynomial:
[tex]\implies 1(2-7x-9x^2)+4x(2-7x-9x^2)+3x^2(2-7x-9x^2)[/tex]
Multiply the monomials from the first polynomial with each term of the second polynomial:
[tex]\implies 2-7x-9x^2+8x-28x^2-36x^3+6x^2-21x^3-27x^4[/tex]
Collect like terms:
[tex]\implies 2+8x-7x-9x^2-28x^2+6x^2-36x^3-21x^3-27x^4[/tex]
Combine like terms:
[tex]\implies 2+x-31x^2-57x^3-27x^4[/tex]
Learn more about products of polynomials here:
https://brainly.com/question/26304770
