Answer :
Answer:
B. [tex] 2 + x - 31x^2 - 57x^3 - 27x^4 [/tex]
Step-by-step explanation:
Given:
- To find the product of: [tex] (1 + 4x + 3x^2)(2 - 7x - 9x^2) [/tex]
Let’s expand this using the distributive property (FOIL or box method). Multiply each term from the first polynomial with each term of the second:
For 1:
- [tex] 1 \cdot 2 = 2 [/tex]
- [tex] 1 \cdot (-7x) = -7x [/tex]
- [tex] 1 \cdot (-9x^2) = -9x^2 [/tex]
For 4x:
- [tex] 4x \cdot 2 = 8x [/tex]
- [tex] 4x \cdot (-7x) = -28x^2 [/tex]
- [tex] 4x \cdot (-9x^2) = -36x^3 [/tex]
For 3x²:
- [tex] 3x^2 \cdot 2 = 6x^2 [/tex]
- [tex] 3x^2 \cdot (-7x) = -21x^3 [/tex]
- [tex] 3x^2 \cdot (-9x^2) = -27x^4 [/tex]
Now, combine like terms:
- Constant: [tex] 2 [/tex]
- x terms: [tex] -7x + 8x = x [/tex]
- x² terms: [tex] -9x^2 -28x^2 + 6x^2 = -31x^2 [/tex]
- x³ terms: [tex] -36x^3 -21x^3 = -57x^3 [/tex]
- x⁴ term: [tex] -27x^4 [/tex]
Therefore, the final answer results in:
[tex] \boxed{2 + x - 31x^2 - 57x^3 - 27x^4} [/tex]