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

2 min read Jun 16, 2024
(a+3)(a-2)-(a+4)(a-3)

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'.

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