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}   } 
Формулы сокращенного умножения
Формулы сокращенного умножения для квадратов, кубов и четвертой степени. Приводим формулы для быстрого использования и вычислений.
Формулы сокращенного умножения для квадратов
| \((a + b)^2 = a^2+ 2ab + b^2\) | – квадрат суммы |
| \((a – b)^2 = a^2 – 2ab + b^2\) | – квадрат разности |
| \(a^2 – b^2 = (a – b)(a + b)\) | – разность квадратов |
Надо запомнить!
Формулы сокращенного умножения для кубов
| \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) | – куб суммы |
| \((a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3\) | – куб разности |
| \(a^3 + b^3 = (a + b)(a^2 – ab + b^2)\) | – сумма кубов |
| \(a^3 – b^3 = (a – b)(a^2 + ab + b^2)\) | – разность кубов |
Формулы сокращенного умножения для четвертой степени
| \((a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4\) |
| \((a – b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4\) |
| \(a^4 – b^4 = (a – b)(a + b)(a^2 + b^2)\) |
Важно знать!
