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Разбор трёх формул: разность квадратов, квадрат суммы, квадрат разности

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Татьяна
Татьяна
Kazakhstan

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Формулы сокращенного умножения
 

Формулы сокращенного умноженияOnline version

Разбор трёх формул: разность квадратов, квадрат суммы, квадрат разности

by Татьяна
1

Введение

2

Разность квадратов

Разность квадратов: a^2 - b^2 = (a - b)(a + b). Подходит для упрощения выражений и упорядочивания множителей.

3

Пример 1: разность квадратов

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Квадрат суммы

Квадрат суммы: (a + b)^2 = a^2 + 2ab + b^2. Показывает связь между суммой и её частями.

5

Пример 2: квадрат суммы

Разложим: (m + n)^2 = m^2 + 2mn + n^2. Используем для факторизации полиномов и расширения выражений.

6

Квадрат разности

Квадрат разности: (a - b)^2 = a^2 - 2ab + b^2. Полезно для распознавания двучастных выражений.

7

Пример 3: квадрат разности

Разложим: (3x - 4)^2 = 9x^2 - 24x + 16. Помогает в упрощении и вычислениях.

8

Сравнение формул

Все формулы связываются: разность квадратов — разложение разности квадратов; квадрат суммы и квадрат разности — квадраты выражения и их удвоенные произведения.

9

Задача на применение

Упростим выражение: (a + b)^2 - (a - b)^2. Используем обе формулы: 4ab. Быстро и без калькулятора.
 
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