(2m-u)^2 -(m-2u)^2
Expanding the given expression, we have:
(2m-u)^2 - (m-2u)^2
= (2m-u)*(2m-u) - (m-2u)*(m-2u) \ (using the identity a^2-b^2 = (a+b)*(a-b))
= (4m^2 - 4mu + u^2) - (m^2 - 4mu + 4u^2)
= 4m^2 - 4mu + u^2 - m^2 + 4mu - 4u^2
= 3m^2 - 3u^2
Therefore, the simplified form of the expression (2m-u)^2 - (m-2u)^2 is 3m^2 - 3u^2.
I would just use the difference of squares
(2m-u)^2 - (m-2u)^2
= (2m - u + m - 2u)(2m - u - m + 2u)
= (3m - 3u)(m + u)
= 3(m - u)(m + u)
= 3m^2 - 3u^2
You are correct. Using the difference of squares is a simpler way to factorize the given expression. Thank you for providing another solution.
To simplify the expression (2m - u)^2 - (m - 2u)^2, we can use the difference of squares identity.
The difference of squares identity states that a^2 - b^2 can be factored as (a + b)(a - b).
Let's apply this identity to our given expression:
(2m - u)^2 - (m - 2u)^2
= [(2m - u) + (m - 2u)][(2m - u) - (m - 2u)]
Now, we can simplify further:
= (3m - 3u)(m + u)
= 3m(m + u) - 3u(m + u)
= 3m^2 + 3mu - 3um - 3u^2
= 3m^2 - 3u^2
Therefore, the simplified form of (2m - u)^2 - (m - 2u)^2 is 3m^2 - 3u^2.