Answer :
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.
### 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.
