High School

Find the product of [tex]2x^4(2x^2 + 3x + 4)[/tex].

A. [tex]2x^8[/tex]
B. [tex]3x^4[/tex]
C. [tex]4x^4[/tex]
D. [tex]4x^6[/tex]
E. [tex]6x^5[/tex]
F. [tex]8x^4[/tex]
G. [tex]4x^4[/tex]
H. [tex]3x^5[/tex]
I. [tex]2x^6[/tex]
J. [tex]3x^6[/tex]
K. [tex]4x^5[/tex]
L. [tex]5x^4[/tex]

Answer :

Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex]2x^4(2x^2 + 3x + 4)[/tex] is [tex]4x^6 + 6x^5 + 8x^4[/tex]

What is distributive property of multiplication over addition?

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The given expression is simplified as:

[tex]2x^4(2x^2 + 3x + 4) = 2x^4 \times 2x^2 + 2x^4 \times 3x + 2x^4 \times 4\\2x^4(2x^2 + 3x + 4) = 4x^6 + 6x^5 + 8x^4[/tex]

Thus,

The product of [tex]2x^4(2x^2 + 3x + 4)[/tex] is [tex]4x^6 + 6x^5 + 8x^4[/tex]

Learn more about product of polynomials here:

https://brainly.com/question/9106484

Answer:

4x^6 + 6x^4 + 8x^4

Step-by-step explanation:

its the only option with a 6 in the 2nd term.