(x-5)^2-3(x+8)

2 min read Jun 17, 2024

Expanding and Simplifying the Expression (x - 5)² - 3(x + 8)

This article will guide you through expanding and simplifying the algebraic expression (x - 5)² - 3(x + 8). We will break down the process step-by-step, ensuring a clear understanding of the solution.

Step 1: Expanding the Square

The first term in the expression is (x - 5)². This is a squared binomial, which means we can expand it using the FOIL method (First, Outer, Inner, Last):

(x - 5)² = (x - 5)(x - 5)

First: x * x = x²
Outer: x * -5 = -5x
Inner: -5 * x = -5x
Last: -5 * -5 = 25

Combining the terms, we get: x² - 5x - 5x + 25

Simplifying: x² - 10x + 25

Step 2: Expanding the Second Term

The second term is -3(x + 8). We distribute the -3 to both terms inside the parentheses:

-3(x + 8) = -3x - 24

Step 3: Combining Like Terms

Now, let's combine the expanded terms from Step 1 and Step 2:

(x² - 10x + 25) + (-3x - 24)

Combining like terms: x² - 13x + 1

Conclusion

Therefore, the simplified form of the expression (x - 5)² - 3(x + 8) is x² - 13x + 1.