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

A. [tex]\( 2x^8 + 3x^4 + 4x^4 \)[/tex]
B. [tex]\( 4x^6 + 6x^5 + 8x^4 \)[/tex]
C. [tex]\( 4x^4 + 3x^5 + 2x^6 \)[/tex]
D. [tex]\( 3x^6 + 4x^5 + 5x^4 \)[/tex]



Answer :

GinnyAnswer
To find the product of [tex]\(2 x^4\left(2 x^2 + 3 x + 4\right)\)[/tex], we will follow the distributive property to expand the polynomial expression.

[tex]\[ 2 x^4 \left(2 x^2 + 3 x + 4\right) \][/tex]

We need to distribute [tex]\(2 x^4\)[/tex] to each term within the parenthesis:

[tex]\[ = 2 x^4 \cdot 2 x^2 + 2 x^4 \cdot 3 x + 2 x^4 \cdot 4 \][/tex]

Let's expand each term separately:

1. [tex]\(2 x^4 \cdot 2 x^2\)[/tex]:
[tex]\[ 2 \cdot 2 \cdot x^4 \cdot x^2 = 4 x^{4+2} = 4 x^6 \][/tex]

2. [tex]\(2 x^4 \cdot 3 x\)[/tex]:
[tex]\[ 2 \cdot 3 \cdot x^4 \cdot x = 6 x^{4+1} = 6 x^5 \][/tex]

3. [tex]\(2 x^4 \cdot 4\)[/tex]:
[tex]\[ 2 \cdot 4 \cdot x^4 = 8 x^4 \][/tex]

Now, combining all these terms together, the expanded polynomial is:

[tex]\[ 4 x^6 + 6 x^5 + 8 x^4 \][/tex]

Therefore, the product of [tex]\(2 x^4 \left(2 x^2 + 3 x + 4\right)\)[/tex] is:

[tex]\[\boxed{4 x^6 + 6 x^5 + 8 x^4}\][/tex]

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