Certainly! Let's simplify the given expression step-by-step:
Given expression:
[tex]\[ a^2 + a \cdot b \cdot (b \cdot 0.1) + b^3 \][/tex]
Step 1: Identify each term in the expression
- The first term is [tex]\( a^2 \)[/tex].
- The second term involves the product [tex]\( a \cdot b \cdot (b \cdot 0.1) \)[/tex].
- The third term is [tex]\( b^3 \)[/tex].
Step 2: Simplify the second term
- Focus on the part inside the second term: [tex]\( b \cdot (b \cdot 0.1) \)[/tex].
- Multiply [tex]\( b \)[/tex] by [tex]\( b \cdot 0.1 \)[/tex] to get [tex]\( b^2 \cdot 0.1 \)[/tex].
Step 3: Incorporate this back into the second term
- Now the second term becomes [tex]\( a \cdot (b^2 \cdot 0.1) \)[/tex], which can be written as [tex]\( 0.1a \cdot b^2 \)[/tex].
Step 4: Combine all the terms
- Now the entire expression is: [tex]\( a^2 + 0.1a \cdot b^2 + b^3 \)[/tex].
So, the simplified version of the given expression is:
[tex]\[ a^2 + 0.1a \cdot b^2 + b^3 \][/tex]
This matches the expression you provided:
[tex]\[
a^2 + 0.1a \cdot b^2 + b^3
\][/tex]
Therefore, our simplified, and final expression is:
[tex]\[ a^2 + 0.1a \cdot b^2 + b^3 \][/tex]
