Find the product of 2x^4(4x^2 + 3x + 1).

We want to find the product:

                         [tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)[/tex].

By the [tex]\text{Distributive property}[/tex], we distribute [tex]2x^4[/tex] over each of the three terms inside the parenthesis:

[tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)=2x^4\cdot4x^2+2x^4\cdot3x+2x^4\cdot1[/tex].

Multiplying the coefficients, and adding the exponents we get:

[tex]8x^6+6x^5+2x^4[/tex].


Answer: [tex]8x^6+6x^5+2x^4[/tex].