%5E2%2B(m%5E2-3)%5E2-2(m%5E2-3)(m%5E3-m%2B1).jpeg "(m^3-m+1)^2+(m^2-3)^2-2(m^2-3)(m^3-m+1)")
Factoring the Expression: (m^3-m+1)^2+(m^2-3)^2-2(m^2-3)(m^3-m+1)
This expression might look intimidating at first, but it's actually a perfect square trinomial in disguise. Let's break it down and simplify it.
Recognizing the Pattern
Notice that the expression resembles the expansion of a squared binomial:
(a - b)² = a² - 2ab + b²
Let's try to identify 'a' and 'b' in our expression:
- a = m^3 - m + 1
- b = m² - 3
Now, let's substitute these values into the expanded form of (a - b)²:
(m^3 - m + 1)² - 2(m^3 - m + 1)(m² - 3) + (m² - 3)²
Simplifying the Expression
We can now clearly see that our original expression is just the expanded form of (a - b)². Therefore, we can simplify it as:
(m^3 - m + 1 - (m² - 3))²
Final Result
Further simplification gives us:
(m^3 - m² - m + 4)²
Therefore, the factored form of the given expression is (m^3 - m² - m + 4)².