Новая Школа - онлайн-школа подготовки к ЕГЭ
Задача Задача №2608378
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Аноним
09 января 2025 18:02 · публичный вопрос
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Аноним

1) (m-3)•(m+3)= 2) (c-7)•(c+7)= 3) (4x+5a)•(5a-4)= 4) (7x-2)•(7x+2)= 5) (8b+5a)•(5a-8b)= 6) (10p-6q)•(10p+6q)=

Ответ нейросети
09 января 2025 18:02

To solve each of these expressions, we will use the difference of squares formula, which states that:

\[ (a - b)(a + b) = a^2 - b^2 \]

Now, let's apply this to each expression:

  1. \((m-3) \cdot (m+3) = m^2 - 3^2 = m^2 - 9\)

  2. \((c-7) \cdot (c+7) = c^2 - 7^2 = c^2 - 49\)

  3. \((4x + 5a)(5a - 4)\) is not in the form of a difference of squares. Let's expand this expression:

\[ (4x + 5a)(5a - 4) = 4x \cdot 5a - 4 \cdot 4x + 5a \cdot 5a - 5a \cdot 4 \] \[ = 20ax - 16x + 25a^2 - 20a \] So, the result is \(20ax - 16x + 25a^2 - 20a\).

  1. \((7x-2) \cdot (7x+2) = (7x)^2 - 2^2 = 49x^2 - 4\)

  2. \((8b + 5a)(5a - 8b)\) is also not in the difference of squares form, so we will expand this as well:

\[ (8b + 5a)(5a - 8b) = 8b \cdot 5a - 8b \cdot 8b + 5a \cdot 5a - 5a \cdot 8b \] \[ = 40ab - 64b^2 + 25a^2 - 40ab \] \[ = 25a^2 - 64b^2 \] So, the result is \(25a^2 - 64b^2\).

  1. \((10p-6q) \cdot (10p+6q) = (10p)^2 - (6q)^2 = 100p^2 - 36q^2\)

In summary, the simplified results are:

  1. \(m^2 - 9\)

  2. \(c^2 - 49\)

  3. \(20ax - 16x + 25a^2 - 20a\)

  4. \(49x^2 - 4\)

  5. \(25a^2 - 64b^2\)

  6. \(100p^2 - 36q^2\)