Of course! Let's solve the given expression step-by-step:
[tex]\[ 7 + 2(3 + 2)^3 + 3\left(4^2 - 20\right) - 8\left(3^2 + 2^3\right) + 2 \][/tex]
First, we will break down and calculate each term separately.
1. First term:
[tex]\[
7
\][/tex]
This term remains as it is.
2. Second term:
[tex]\[
2(3 + 2)^3
\][/tex]
- First, solve the expression inside the parentheses:
[tex]\[
3 + 2 = 5
\][/tex]
- Next, raise 5 to the power of 3:
[tex]\[
5^3 = 125
\][/tex]
- Then, multiply by 2:
[tex]\[
2 \times 125 = 250
\][/tex]
3. Third term:
[tex]\[
3\left(4^2 - 20\right)
\][/tex]
- First, calculate [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
- Next, subtract 20 from 16:
[tex]\[
16 - 20 = -4
\][/tex]
- Then, multiply by 3:
[tex]\[
3 \times -4 = -12
\][/tex]
4. Fourth term:
[tex]\[
-8\left(3^2 + 2^3\right)
\][/tex]
- First, calculate [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
- Next, calculate [tex]\(2^3\)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
- Then, add the results:
[tex]\[
9 + 8 = 17
\][/tex]
- Finally, multiply by -8:
[tex]\[
-8 \times 17 = -136
\][/tex]
5. Fifth term:
[tex]\[
2
\][/tex]
This term remains as it is.
Now, let's sum up all the terms we have calculated:
[tex]\[
7 + 250 + (-12) + (-136) + 2
\][/tex]
Combine the terms step-by-step:
[tex]\[
7 + 250 = 257
\][/tex]
[tex]\[
257 - 12 = 245
\][/tex]
[tex]\[
245 - 136 = 109
\][/tex]
[tex]\[
109 + 2 = 111
\][/tex]
So, the final result of the expression is:
[tex]\[
\boxed{111}
\][/tex]
