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What is the product?

[tex]\[ 3x^5 \left(2x^2 + 4x + 1\right) \][/tex]

A. [tex]\[ 2x^7 + 4x^6 + x^5 \][/tex]

B. [tex]\[ 6x^{10} + 12x^5 + 3x^5 \][/tex]

C. [tex]\[ 6x^7 + 12x^6 + 3x^5 \][/tex]

D. [tex]\[ 3x^5 + 2x^2 + 4x + 1 \][/tex]



Answer :

GinnyAnswer
Certainly! Let's find the product of the expression:

[tex]\[ 3x^5 \left(2x^2 + 4x + 1\right) \][/tex]

We need to distribute [tex]\(3x^5\)[/tex] to each term within the parentheses:

1. Distribute [tex]\(3x^5\)[/tex] to [tex]\(2x^2\)[/tex]:
[tex]\[ 3x^5 \cdot 2x^2 = 6x^{5+2} = 6x^7 \][/tex]

2. Distribute [tex]\(3x^5\)[/tex] to [tex]\(4x\)[/tex]:
[tex]\[ 3x^5 \cdot 4x = 12x^{5+1} = 12x^6 \][/tex]

3. Distribute [tex]\(3x^5\)[/tex] to [tex]\(1\)[/tex]:
[tex]\[ 3x^5 \cdot 1 = 3x^5 \][/tex]

Now, combine all these results together:

[tex]\[ 6x^7 + 12x^6 + 3x^5 \][/tex]

Thus, the expanded expression is:

[tex]\[ 6x^7 + 12x^6 + 3x^5 \][/tex]

So the correct answer is:

[tex]\[ 6x^7 + 12x^6 + 3x^5 \][/tex]

This corresponds to the option:

[tex]\[ \boxed{6x^7 + 12x^6 + 3x^5} \][/tex]

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