Question

What is the value of the expression c2(8−b+a3)+7⋅a
when a=2
, b=4
, and c=3
?

Answer 1

To evaluate the expression \( c^2(8 - b + a^3) + 7 \cdot a \) with the values \( a = 2 \), \( b = 4 \), and \( c = 3 \), we will substitute these values into the expression step by step.

1. Substitute the values into the expression:
\[
c^2(8 - b + a^3) + 7 \cdot a = 3^2(8 - 4 + 2^3) + 7 \cdot 2
\]

2. Calculate \( c^2 \):
\[
c^2 = 3^2 = 9
\]

3. Calculate \( a^3 \):
\[
a^3 = 2^3 = 8
\]

4. Substitute \( b \) and calculate the expression inside the parentheses:
\[
8 - b + a^3 = 8 - 4 + 8 = 4 + 8 = 12
\]

5. Now we have:
\[
9(12) + 7 \cdot 2
\]

6. Calculate \( 9 \cdot 12 \):
\[
9 \cdot 12 = 108
\]

7. Calculate \( 7 \cdot 2 \):
\[
7 \cdot 2 = 14
\]

8. Now sum the results:
\[
108 + 14 = 122
\]

Thus, the value of the expression is \(\boxed{122}\).