Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Simplify the following expressions:

[tex]
2 \times (6x^7 + 9x^2 + 61)
[/tex]

[tex]
2 \times 9 \times 6t
[/tex]

Absolutely! Let's work out each expression step-by-step and find their simplified forms.

### Expression 1: [tex]\(2 \times (6x^7 + 9x^2 + 61)\)[/tex]

To simplify this expression, we need to distribute the 2 across each term inside the parentheses:

[tex]\[
2 \times (6x^7 + 9x^2 + 61)
\][/tex]

First, distribute the 2 to [tex]\(6x^7\)[/tex]:

[tex]\[
2 \times 6x^7 = 12x^7
\][/tex]

Next, distribute the 2 to [tex]\(9x^2\)[/tex]:

[tex]\[
2 \times 9x^2 = 18x^2
\][/tex]

Lastly, distribute the 2 to 61:

[tex]\[
2 \times 61 = 122
\][/tex]

Now, combine these results:

[tex]\[
12x^7 + 18x^2 + 122
\][/tex]

### Expression 2: [tex]\(2 \times 9 \times 6t\)[/tex]

To simplify this expression, multiply the constants 2, 9, and 6:

[tex]\[
2 \times 9 = 18
\][/tex]

Then multiply the result by 6:

[tex]\[
18 \times 6 = 108
\][/tex]

Finally, multiply this result by [tex]\(t\)[/tex]:

[tex]\[
108 \times t = 108t
\][/tex]

### Summary

So, the simplified forms of the given expressions are:

1. [tex]\(12x^7 + 18x^2 + 122\)[/tex]
2. [tex]\(108t\)[/tex]

These are the simplified results for each expression.