2.jpeg "(m2-2m-1)2")
Expanding and Simplifying (m^2 - 2m - 1)^2
The expression (m^2 - 2m - 1)^2 represents the square of a trinomial. To simplify it, we can use the following steps:
Understanding the Problem
We need to expand the expression (m^2 - 2m - 1)^2. This means multiplying the trinomial (m^2 - 2m - 1) by itself.
Applying the Distributive Property
We can use the distributive property to expand the expression. This property states that a(b + c) = ab + ac. In our case, we have:
(m^2 - 2m - 1)^2 = (m^2 - 2m - 1)(m^2 - 2m - 1)
Now, we need to multiply each term in the first trinomial by each term in the second trinomial:
m^2 * (m^2 - 2m - 1) - 2m * (m^2 - 2m - 1) - 1 * (m^2 - 2m - 1)
Expanding and Combining Like Terms
Next, we need to expand each product:
m^4 - 2m^3 - m^2 - 2m^3 + 4m^2 + 2m - m^2 + 2m + 1
Finally, we combine like terms:
m^4 - 4m^3 + 2m^2 + 4m + 1
Final Answer
Therefore, the simplified form of (m^2 - 2m - 1)^2 is m^4 - 4m^3 + 2m^2 + 4m + 1.