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

Verified step by step guidance

1. Identify the expression to be rewritten: \(-7(x - 4y)\).
2. Recognize that the distributive property allows you to multiply a single term by each term inside the parentheses.
3. Apply the distributive property: multiply \(-7\) by each term inside the parentheses \((x - 4y)\).
4. Calculate \(-7 \times x\) to get \(-7x\).
5. Calculate \(-7 \times (-4y)\) to get \(+28y\).

Key Concepts

Distributive Property

The distributive property states that for any numbers a, b, and c, the expression a(b + c) can be rewritten as ab + ac. This property allows us to multiply a single term by each term within a parenthesis, effectively distributing the multiplication across the terms.

Negative Coefficients

A negative coefficient indicates that the term it multiplies will be negated. For example, in the expression -7(x - 4y), the -7 will change the signs of both x and -4y when distributed, resulting in -7x + 28y. Understanding how to handle negative coefficients is crucial for accurate simplification.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. In the context of the distributive property, after distributing, it’s important to identify and combine any like terms to achieve the simplest form of the expression.