%5E2-4(x%2B2y-3)%2B4.jpeg "(x+2y-3)^2-4(x+2y-3)+4")
Factoring a Quadratic Expression: (x + 2y - 3)^2 - 4(x + 2y - 3) + 4
This expression might look complicated at first glance, but it can be simplified by recognizing a pattern and using algebraic techniques.
Identifying the Pattern
Notice that the expression has the following structure:
- (something)^2 - 4(something) + 4
This structure strongly resembles the pattern of a perfect square trinomial:
- (a - b)^2 = a^2 - 2ab + b^2
Applying the Pattern
Let's identify the 'a' and 'b' terms in our expression:
- a = (x + 2y - 3)
- b = 2
Now, we can rewrite the expression using the perfect square trinomial pattern:
- (x + 2y - 3)^2 - 4(x + 2y - 3) + 4 = (x + 2y - 3 - 2)^2
Simplifying the Expression
Finally, simplify the expression:
- (x + 2y - 3 - 2)^2 = (x + 2y - 5)^2
Conclusion
By recognizing the pattern of a perfect square trinomial, we were able to factor the given expression and simplify it to (x + 2y - 5)^2.