(a+3)(a-2)-(a+4)(a-3)

2 min read Jun 16, 2024

Expanding and Simplifying the Expression (a+3)(a-2)-(a+4)(a-3)

This article will guide you through the process of expanding and simplifying the algebraic expression: (a+3)(a-2)-(a+4)(a-3).

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)(a-2):
- 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)(a-3):
- 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)(a-2)-(a+4)(a-3) = (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)(a-2)-(a+4)(a-3), we arrive at the final answer: 6. This means that the expression is a constant, independent of the value of 'a'.