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Коли працюєш зi змiнними та дужками, потрiбно дотримуватися певного набору правил. Цi правила допоможуть розкрити дужки, щоб очистити вираз. У школi роботi з подiбними виразами присвячується чимало часу, тож уважно стеж за процесом.

Правило

Множення чисел та знакiв на дужки

1.: Знак $+$ перед дужками не змiнює виразу в дужках.
2.: Знак $-$ перед дужками змiнює всi знаки в дужках.
3.: Якщо помножити дужки на додатний множник, знаки не змiнюються, але доданки в дужках множаться на множник за дужками.
4.: Якщо помножити дужки на вiд’ємний множник, змiняться всi знаки в дужках, а доданки в дужках множаться на множник за дужками.

Ось кiлька прикладiв, якi iлюструють чотири правила, наведенi вище:

Приклад 1

Правило 1

Розкрий дужки:

+ (x + 1) = x + 1

Розкрий дужки:

+ (x - 1) = x - 1

Розкрий дужки:

+ (- x - 1) = - x - 1

Розкрий дужки:

+ (- x + 1) = - x + 1

Приклад 2

Правило 2

Розкрий дужки:

- (x + 1) = - + x - + 1 = - x - 1

Розкрий дужки:

- (x - 1) = - + x - - 1 = - x + 1

Розкрий дужки:

- (- x - 1) = - - x - - 1 = x + 1

Розкрий дужки:

- (- x + 1) = - - x - + 1 = x - 1

Приклад 3

Правило 3

Розкрий дужки:

\begin{array}{c} 2 a & = + + 2 a \cdot a + + 2 a \cdot 3 \\ = 2 a^{2} + 6 a \end{array}

2 a

Розкрий дужки:

\begin{array}{c} 2 a & = + + 2 a \cdot a + - 2 a \cdot 3 \\ = 2 a^{2} - 6 a \end{array}

2 a

Розкрий дужки:

\begin{array}{c} 2 a & = + - 2 a \cdot a + - 2 a \cdot 3 \\ = - 2 a^{2} - 6 a \end{array}

2 a

Розкрий дужки:

\begin{array}{c} 2 a & = + - 2 a \cdot a + + 2 a \cdot 3 \\ = - 2 a^{2} + 6 a \end{array}

2 a

Приклад 4

Правило 4

Розкрий дужки:

\begin{array}{c} - a & = - + a \cdot b - + a \cdot a \\ = - a b - a^{2} \end{array}

- a

Розкрий дужки:

\begin{array}{c} - a & = - + a \cdot b - - a \cdot a \\ = - a b + a^{2} \end{array}

- a

Розкрий дужки:

\begin{array}{c} - a & = - - a \cdot b - - a \cdot a \\ = a b + a^{2} \end{array}

- a

Розкрий дужки:

\begin{array}{c} - a & = - - a \cdot b - + a \cdot a \\ = a b - a^{2} \end{array}

- a

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