## Factoring the Expression (x+4)² - 5xy - 20y - 6y²

This article will guide you through the process of factoring the expression (x+4)² - 5xy - 20y - 6y².

### Step 1: Expanding the Square

Begin by expanding the squared term:

(x + 4)² = x² + 8x + 16

Now, the expression becomes: x² + 8x + 16 - 5xy - 20y - 6y²

### Step 2: Grouping Terms

Group the terms with common factors:

(x² - 5xy) + (8x - 20y) + (16 - 6y²)

### Step 3: Factoring by Grouping

Factor out the greatest common factor (GCF) from each group:

**x(x - 5y) + 4(2x - 5y) + 2(8 - 3y²)**

### Step 4: Identifying the Common Binomial

Notice that the binomial (x - 5y) appears in both the first and second terms.

**(x - 5y)(x + 4) + 2(8 - 3y²)**

### Step 5: Final Factorization

Unfortunately, the expression cannot be factored further. However, it has been simplified to a form with two terms:

**(x - 5y)(x + 4) + 2(8 - 3y²)**

This is the factored form of the original expression (x+4)² - 5xy - 20y - 6y².

### Conclusion

Factoring algebraic expressions often involves multiple steps. By carefully applying the techniques of expanding, grouping, and factoring out common factors, we can successfully factor complex expressions into simpler forms. While the final form of this expression may not be fully factorable, the process demonstrates the power of these methods.