To evaluate the expression [tex]\(3(a + b)^2 - 5a\)[/tex] when [tex]\(a = 7\)[/tex] and [tex]\(b = 1\)[/tex], let's follow the step-by-step process:
1. Substitute the given values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[
3(7 + 1)^2 - 5 \cdot 7
\][/tex]
2. First, calculate the sum inside the parentheses:
[tex]\[
7 + 1 = 8
\][/tex]
3. Next, square this result:
[tex]\[
8^2 = 64
\][/tex]
4. Now, multiply this squared result by 3:
[tex]\[
3 \cdot 64 = 192
\][/tex]
5. Then, calculate the product of 5 and [tex]\(a\)[/tex] (which is 7):
[tex]\[
5 \cdot 7 = 35
\][/tex]
6. Finally, subtract this product from the previous result:
[tex]\[
192 - 35 = 157
\][/tex]
So, the simplified value of the expression [tex]\(3(a + b)^2 - 5a\)[/tex] when [tex]\(a = 7\)[/tex] and [tex]\(b = 1\)[/tex] is [tex]\(\boxed{157}\)[/tex].
