Failing to use parentheses (sometimes due to pure laziness) often leads to mistakes.

Why do we even sometimes need parentheses? The answer is that they help control the proper order of operations. Consider the difference between

2 + 3 × 4 = 2 + 12 = 14

and

(2 + 3) × 4 = 6 × 4 = 24.

In the first calculation the multiplication is done first and then the addition, even though the addition appears first reading left to right. This is because there's a convention (a rule) that multiplication has a higher precedence than addition. We use parentheses to force the addition to be done first. We say parentheses have higher precedence than multiplication.

For the examples, let f(x) = 3x and g(x) = 4x-3.

Example 1: Expand f(x)g(x).

Mistake:

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f(x) = 3x must distribute over both terms of g(x). We use parentheses to show that this must be done. Failing to write the parentheses often results in forgetting to distribute correctly.

Example 2: Simplify f(x) - g(x).

Mistake:

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The subtraction must distribute over both terms of g(x), which is why parentheses are required.

Use and take care with parentheses!