Новая Школа - онлайн-школа подготовки к ЕГЭ
Задача Задача №2643303
А
Аноним
19 января 2025 13:52 · публичный вопрос
А
Аноним

(2-m)(-m-2)-(5+m)²

Ответ нейросети
19 января 2025 13:52

To simplify the expression \((2-m)(-m-2)-(5+m)^{2}\), let's break it down step by step.

  1. Expand the first part \((2-m)(-m-2)\):

    \[ (2-m)(-m-2) = 2 \cdot (-m) + 2 \cdot (-2) + (-m) \cdot (-m) + (-m) \cdot (-2) \]

    This results in:

    \[ = -2m - 4 + m^2 + 2m \]

    Now, combine the like terms:

    \[ -2m + 2m - 4 + m^2 = m^2 - 4 \]

  2. Expand the second part \((5+m)^{2}\):

    \[ (5+m)^{2} = 5^2 + 2 \cdot 5 \cdot m + m^2 = 25 + 10m + m^2 \]

  3. Put it all together: Now, substituting our expansions into the original expression gives us:

    \[ (2-m)(-m-2)-(5+m)^{2} = (m^2 - 4) - (25 + 10m + m^2) \]

  4. Distributing the negative sign:

    \[ = m^2 - 4 - 25 - 10m - m^2 \]

  5. Combine like terms: The \(m^2\) terms cancel out:

    \[ = -4 - 25 - 10m = -29 - 10m \]

So, the final simplified expression is:

\[ \boxed{-29 - 10m} \]