Question

(m² - n) (m² + n²) - m (m² - n) - mn²=-nx^{2}

Answer 1

Ответ:

тождество неверное____

Answer 2

Let's simplify the given expression step by step:

(m² - n) (m² + n²) - m (m² - n) - mn²

First, let's factor out the common term (m² - n) from the first two terms:

(m² - n) [(m² + n²) - m]

Now, we can expand the second term inside the parentheses:

(m² - n) [m² + n² - m]

Next, let's distribute the (m² - n) into the expanded expression:

m⁴ + mn² - m³ - n²m - m²n + mn

Now, let's simplify further:

m⁴ - m³ + mn² - m²n - n²m + mn

Now, let's group like terms:

(m⁴ - m³) + (mn² - n²m) + mn

Factor out common terms from each group:

m³(m - 1) - n²(m - 1) + mn

Notice that we have a common factor of (m - 1) in the first two terms:

(m - 1)(m³ - n²) + mn

Now, we can factor further if needed, but this is the simplified form of the expression:

(m - 1)(m³ - n²) + mn = -nx²