2-6(x-2y)%2B5.jpeg "(x-2y)2-6(x-2y)+5")
Factoring the Expression (x-2y)² - 6(x-2y) + 5
This expression can be factored using a substitution method and the knowledge of factoring quadratic equations.
Step 1: Substitution
Let's substitute u = (x-2y). This simplifies our expression to:
u² - 6u + 5
Step 2: Factoring the Quadratic Expression
Now, we have a standard quadratic expression. We need to find two numbers that:
- Multiply to give 5 (the constant term)
- Add to give -6 (the coefficient of the middle term)
The numbers -1 and -5 satisfy these conditions:
- (-1) * (-5) = 5
- (-1) + (-5) = -6
Therefore, we can factor the quadratic as:
(u - 1)(u - 5)
Step 3: Back-Substitution
Now, substitute back (x-2y) for u:
[(x-2y) - 1] [(x-2y) - 5]
Step 4: Simplify
Simplify the expression:
(x - 2y - 1)(x - 2y - 5)
Final Answer:
The factored form of the expression (x-2y)² - 6(x-2y) + 5 is (x - 2y - 1)(x - 2y - 5).