2-2(2a-3)(a-1)%2B(a-1)2.jpeg "(2a-3)2-2(2a-3)(a-1)+(a-1)2")
Factoring the Expression (2a-3)2-2(2a-3)(a-1)+(a-1)2
This expression might look intimidating at first, but it's actually a perfect square trinomial in disguise. Let's break down how to factor it:
Recognizing the Pattern
The expression follows the pattern of a perfect square trinomial:
(x - y)2 = x2 - 2xy + y2
In our case:
- x = (2a - 3)
- y = (a - 1)
Applying the Pattern
Let's substitute these values into the pattern:
- x2 = (2a - 3)2
- 2xy = 2(2a - 3)(a - 1)
- y2 = (a - 1)2
We can see that our expression matches the perfect square trinomial pattern perfectly!
Factoring the Expression
Now we can apply the pattern to factor the expression:
(2a - 3)2 - 2(2a - 3)(a - 1) + (a - 1)2 = [(2a - 3) - (a - 1)]2
Simplifying the Result
Let's simplify the factored expression:
- [(2a - 3) - (a - 1)]2 = (2a - 3 - a + 1)2
- (2a - 3 - a + 1)2 = (a - 2)2
Final Answer
Therefore, the factored form of the expression (2a-3)2-2(2a-3)(a-1)+(a-1)2 is (a - 2)2.