Certainly! Let's solve the expression [tex]\( a y^2 - y^3 \)[/tex] step-by-step for [tex]\( a = 8.8 \)[/tex] and [tex]\( y = -1.2 \)[/tex].
1. Substitute the given values into the expression:
[tex]\[
8.8 \cdot (-1.2)^2 - (-1.2)^3
\][/tex]
2. Calculate [tex]\( (-1.2)^2 \)[/tex]:
[tex]\[
(-1.2)^2 = 1.44
\][/tex]
3. Multiply [tex]\( 8.8 \)[/tex] by [tex]\( 1.44 \)[/tex]:
[tex]\[
8.8 \cdot 1.44 = 12.672
\][/tex]
This is the value of the term [tex]\( a y^2 \)[/tex].
4. Calculate [tex]\( (-1.2)^3 \)[/tex]:
[tex]\[
(-1.2)^3 = -1.728
\][/tex]
Note that the actual cubic value is very close to [tex]\(-1.728\)[/tex], but we need to maintain accuracy with significant digits.
5. Form the expression with the two calculated terms:
[tex]\[
12.672 - (-1.728)
\][/tex]
6. Subtract the cubic term (keep in mind subtracting a negative value means adding its positive counterpart):
[tex]\[
12.672 + 1.728 = 14.4
\][/tex]
Therefore, the answer is [tex]\( 14.4 \)[/tex].
So, to summarize:
- The term [tex]\( a y^2 \)[/tex] evaluates to [tex]\( 12.672 \)[/tex].
- The term [tex]\( y^3 \)[/tex] evaluates to [tex]\( -1.728 \)[/tex].
- Subtracting [tex]\( y^3 \)[/tex] from [tex]\( a y^2 \)[/tex], we get the final result of [tex]\( 14.4 \)[/tex].
