(a-5)^2-(a-8)^2

less than a minute read Jun 16, 2024

Simplifying the Expression (a-5)² - (a-8)²

This article aims to simplify the expression (a-5)² - (a-8)². We will achieve this by applying the difference of squares formula and simplifying the resulting expression.

Difference of Squares Formula

The difference of squares formula states that: a² - b² = (a + b)(a - b)

Applying the Formula

Let's apply the difference of squares formula to our expression:

(a - 5)² - (a - 8)² = [(a - 5) + (a - 8)][(a - 5) - (a - 8)]

Simplifying the Expression

Now we can simplify the expression by combining like terms within the brackets:

[(a - 5) + (a - 8)][(a - 5) - (a - 8)] = (2a - 13)(3)

Finally, we can distribute the 3:

(2a - 13)(3) = 6a - 39

Conclusion

Therefore, the simplified expression of (a-5)² - (a-8)² is 6a - 39.