Rewrite each expression using the distributive property and simplify, if possible. See Example 7. -12(x - y)

Verified step by step guidance

1. Identify the distributive property formula: \(a(b - c) = ab - ac\). This means you multiply the term outside the parentheses by each term inside the parentheses.
2. Apply the distributive property to the expression \(-12(x - y)\) by multiplying \(-12\) with \(x\) and then with \(-y\) separately.
3. Calculate the products: \(-12 \times x\) and \(-12 \times (-y)\), remembering that multiplying two negatives results in a positive.
4. Write the expression after distribution: \(-12x + 12y\).
5. Check if the expression can be simplified further by combining like terms or factoring, which in this case it cannot, so the expression \(-12x + 12y\) is the simplified form.

Key Concepts

Distributive Property

The distributive property states that multiplying a number by a sum or difference inside parentheses is equivalent to multiplying the number by each term separately and then adding or subtracting the results. For example, a(b + c) = ab + ac.

Simplifying Algebraic Expressions

Simplifying involves combining like terms and performing arithmetic operations to write an expression in its simplest form. After distribution, terms with the same variables and exponents can be combined to reduce complexity.

Handling Negative Signs in Distribution

When distributing a negative number across terms inside parentheses, the sign of each term changes accordingly. For example, distributing -12 over (x - y) means multiplying -12 by x and -12 by -y, paying attention to sign changes.