Question
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Answer
Упрощенное выражение: \( (a + 2b)(x - 3y) \)
Solution
Давайте упростим выражение:
\[ 2bx - 3ay - 6by + ax \]
**Шаг 1: Перегруппируем подобные слагаемые.**
\[ (2bx + ax) + (-3ay - 6by) \]
**Шаг 2: Вынесем общий множитель из каждой группы.**
\[ x(2b + a) + y(-3a - 6b) \]
**Шаг 3: Упростим коэффициенты внутри скобок.**
\[ x(a + 2b) - 3y(a + 2b) \]
**Шаг 4: Вынесем общий множитель \((a + 2b)\).**
\[ (a + 2b)(x - 3y) \]
**Итоговое упрощенное выражение:**
\[ (a + 2b)(x - 3y) \]
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Simplify this solution Beyond the Answer
To solve the expression \( 2 b x - 3 a y - 6 b y + a x \), you can start by rearranging and grouping the terms by variables. Combine like terms to simplify it: Group \(x\) terms together: \( (2b + a)x \) and group \(y\) terms together: \( (-3a - 6b)y \). So the final simplified expression becomes \( (2b + a)x + (-3a - 6b)y \). This method not only simplifies your work but can also help you spot patterns or factoring opportunities! When tackling expressions like this, watch out for signs and remembering to combine only like terms. A common mistake is omitting coefficients when combining, which can lead to completely different answers. Always double-check your grouping!
