College

Multiply:

[tex]3 x^6\left(12 x^7 - 7 x^6 + 6\right)[/tex]

Options:

A. [tex]36 x^{13} - 7 x^6 + 6[/tex]

B. [tex]36 x^{13} - 21 x^{12} + 18 x^6[/tex]

C. [tex]36 x^7 - 21 x^6 + 18[/tex]

D. [tex]36 x^{13} - 21 x^{12}[/tex]

Answer :

Sure! Let's go through the steps to solve the problem of multiplying the terms:

We have the expression:
[tex]\[ 3x^6(12x^7 - 7x^6 + 6) \][/tex]

To multiply, we'll distribute the term [tex]\(3x^6\)[/tex] across each term inside the parentheses.

1. Multiply [tex]\(3x^6\)[/tex] by [tex]\(12x^7\)[/tex]:
[tex]\[
3x^6 \times 12x^7 = 36x^{6+7} = 36x^{13}
\][/tex]

2. Multiply [tex]\(3x^6\)[/tex] by [tex]\(-7x^6\)[/tex]:
[tex]\[
3x^6 \times -7x^6 = -21x^{6+6} = -21x^{12}
\][/tex]

3. Multiply [tex]\(3x^6\)[/tex] by [tex]\(6\)[/tex]:
[tex]\[
3x^6 \times 6 = 18x^6
\][/tex]

Now, combine all the terms together:
[tex]\[ 36x^{13} - 21x^{12} + 18x^6 \][/tex]

So, the result of multiplying the expression is:
[tex]\[ 36x^{13} - 21x^{12} + 18x^6 \][/tex]

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