CONCEPT PREVIEW Rewrite the expression -7(x - 4y) using the distributive property.

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Identify the distributive property, which states that for any numbers a, b, and c, the expression a(b + c) can be rewritten as ab + ac. In this problem, the expression is -7(x - 4y), where -7 is the factor outside the parentheses.

Apply the distributive property by multiplying -7 with each term inside the parentheses separately. This means you will multiply -7 by x and then -7 by -4y.

Multiply -7 by x to get the first term: \(-7 \times x = -7x\).

Multiply -7 by -4y to get the second term: \(-7 \times (-4y) = 28y\) (note the negative signs cancel out).

Combine the two results to write the expression without parentheses: \(-7x + 28y\).

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주요 개념

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Distributive Property

The distributive property states that multiplying a sum or difference by a number is the same as multiplying each term inside the parentheses by that number separately. For example, a(b + c) = ab + ac. This property helps simplify expressions by removing parentheses.

Multiplication of Negative Numbers

When multiplying a negative number by a positive number, the result is negative. For example, -7 × 4 = -28. Understanding this rule is essential when distributing a negative coefficient across terms inside parentheses.

Combining Like Terms

After applying the distributive property, terms with the same variables and exponents can be combined to simplify the expression. Recognizing like terms helps in rewriting expressions in their simplest form.