Expanding and Simplifying the Expression (a+3)(a2)(a+4)(a3)
This article will guide you through the process of expanding and simplifying the algebraic expression: (a+3)(a2)(a+4)(a3).
Step 1: Expanding the Products
We'll use the FOIL method (First, Outer, Inner, Last) to expand each of the products in the expression:

(a+3)(a2):
 First: a * a = a²
 Outer: a * 2 = 2a
 Inner: 3 * a = 3a
 Last: 3 * 2 = 6
 Combining terms: a²  2a + 3a  6 = a² + a  6

(a+4)(a3):
 First: a * a = a²
 Outer: a * 3 = 3a
 Inner: 4 * a = 4a
 Last: 4 * 3 = 12
 Combining terms: a²  3a + 4a  12 = a² + a  12
Step 2: Combining the Expanded Expressions
Now we substitute the expanded forms back into the original expression:
(a+3)(a2)(a+4)(a3) = (a² + a  6)  (a² + a  12)
Step 3: Simplifying the Expression
Finally, we simplify the expression by removing the parentheses and combining like terms:
 (a² + a  6)  (a² + a  12) = a² + a  6  a²  a + 12
 Combining like terms: (a²  a²) + (a  a) + (6 + 12) = 6
Conclusion
After expanding and simplifying the expression (a+3)(a2)(a+4)(a3), we arrive at the final answer: 6. This means that the expression is a constant, independent of the value of 'a'.