Rewrite each expression using the distributive property and simplify, if possible. See Example 7. -(2d - f)

검증된 단계별 안내

Recognize that the distributive property allows you to multiply a factor outside the parentheses by each term inside the parentheses. Here, the factor is \(-1\) because of the negative sign before the parentheses.

Apply the distributive property: multiply \(-1\) by each term inside the parentheses \(2d - f\). This gives \(-1 \times 2d\) and \(-1 \times (-f)\).

Calculate each multiplication separately: \(-1 \times 2d = -2d\) and \(-1 \times (-f) = +f\) because multiplying two negatives results in a positive.

Rewrite the expression by combining the results from the previous step: \(-2d + f\).

Check if the expression can be simplified further. Since \(-2d\) and \(f\) are unlike terms, the expression \(-2d + f\) is already simplified.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Distributive Property

The distributive property states that multiplying a number by a sum or difference is the same as multiplying each term inside the parentheses separately and then adding or subtracting the results. For example, a(b + c) = ab + ac. This property is essential for rewriting expressions like -(2d - f).

Handling Negative Signs

When a negative sign precedes parentheses, it acts as multiplying the entire expression inside by -1. This means each term inside the parentheses changes its sign when the parentheses are removed. For example, -(2d - f) becomes -2d + f.

Simplifying Algebraic Expressions

Simplifying involves combining like terms and reducing the expression to its simplest form. After applying the distributive property and handling signs, check if any terms can be combined to make the expression clearer and more concise.