To find the value of [tex]\( (9.8)^2 \)[/tex] using the identity [tex]\( (a - b)^2 = a^2 - 2ab + b^2 \)[/tex], let's follow a step-by-step approach.
First, identify the given values:
- [tex]\( a = 9.8 \)[/tex]
- [tex]\( b = 0 \)[/tex]
We can use the identity:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Substitute [tex]\( a = 9.8 \)[/tex] and [tex]\( b = 0 \)[/tex] into the identity:
[tex]\[
(9.8 - 0)^2 = 9.8^2 - 2 \cdot 9.8 \cdot 0 + 0^2
\][/tex]
Simplifying each term individually:
1. Calculate [tex]\( 9.8^2 \)[/tex]:
[tex]\[
9.8^2 = 96.04000000000002
\][/tex]
2. Calculate [tex]\( 2 \cdot 9.8 \cdot 0 \)[/tex]:
[tex]\[
2 \cdot 9.8 \cdot 0 = 0.0
\][/tex]
3. Calculate [tex]\( 0^2 \)[/tex]:
[tex]\[
0^2 = 0
\][/tex]
Now, sum the results obtained from each term:
[tex]\[
9.8^2 - 2 \cdot 9.8 \cdot 0 + 0^2 = 96.04000000000002 - 0.0 + 0
\][/tex]
Combining all terms, we get:
[tex]\[
96.04000000000002
\][/tex]
Thus, the value of [tex]\( (9.8)^2 \)[/tex] is:
[tex]\[
96.04000000000002
\][/tex]
