Let's solve the expression [tex]\(122^8 - 3b^2\)[/tex] assuming [tex]\(b = 2\)[/tex] by following these steps:
1. Calculate [tex]\(122^8\)[/tex]:
We need to evaluate the expression [tex]\(122\)[/tex] raised to the power of 8.
[tex]\[
122^8 = 49077072127303936
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]:
Given [tex]\(b = 2\)[/tex], we square [tex]\(b\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
3. Calculate [tex]\(3b^2\)[/tex]:
We then multiply 3 by [tex]\(b^2\)[/tex]:
[tex]\[
3 \times 4 = 12
\][/tex]
4. Subtract [tex]\(3b^2\)[/tex] from [tex]\(122^8\)[/tex]:
Finally, we subtract [tex]\(12\)[/tex] from [tex]\(49077072127303936\)[/tex]:
[tex]\[
49077072127303936 - 12 = 49077072127303924
\][/tex]
Thus, the expression [tex]\(122^8 - 3b^2\)[/tex] when [tex]\(b = 2\)[/tex] evaluates to:
[tex]\[
49077072127303924
\][/tex]
