To solve the expression [tex]\(2a \left(3b^2 - ab + 40\right)\)[/tex], let's follow a step-by-step approach for simplification.
### Step-by-Step Solution
1. Identify the expression to be simplified:
[tex]\[
2a \left(3b^2 - ab + 40\right)
\][/tex]
2. Distribute the factor [tex]\(2a\)[/tex] to each term inside the parentheses:
Use the distributive property [tex]\(a(b + c + d) = ab + ac + ad\)[/tex].
3. First term:
[tex]\(2a \times 3b^2\)[/tex]:
[tex]\[
2a \cdot 3b^2 = 6ab^2
\][/tex]
4. Second term:
[tex]\(2a \times (-ab)\)[/tex]:
[tex]\[
2a \cdot (-ab) = -2a^2b
\][/tex]
5. Third term:
[tex]\(2a \times 40\)[/tex]:
[tex]\[
2a \cdot 40 = 80a
\][/tex]
6. Combine all the terms together:
Collecting the results from steps 3, 4, and 5, we get:
[tex]\[
6ab^2 - 2a^2b + 80a
\][/tex]
### Conclusion
Simplifying the given expression leads to:
[tex]\[
2a \left(3b^2 - ab + 40\right) = 6ab^2 - 2a^2b + 80a
\][/tex]
Thus, the algebraic form of the expression [tex]\(2a(3b^2 - ab + 40)\)[/tex] is:
[tex]\[
2a(-ab + 3b^2 + 40)
\][/tex]
