Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 2 (x - 3y + 2z)

Verified step by step guidance

1. Identify the distributive property, which states that for any numbers or expressions \(a\), \(b\), and \(c\), \(a(b + c) = ab + ac\). In this problem, the expression is \$2 (x - 3y + 2z)$, where 2 is the factor to distribute.
2. Apply the distributive property by multiplying 2 with each term inside the parentheses separately: \(2 \times x\), \(2 \times (-3y)\), and \(2 \times 2z\).
3. Write the expression after distribution as \$2x - 6y + 4z$ by performing the multiplication for each term.
4. Check if the expression can be simplified further by combining like terms. Since \$2x\(, \)-6y\(, and \)4z$ are unlike terms, no further simplification is possible.
5. Write the final simplified expression as \$2x - 6y + 4z$.

Key Concepts

Distributive Property

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

Combining Like Terms

After distributing, terms with the same variables and exponents can be combined to simplify the expression. For instance, 2x + 3x can be combined to 5x. This step reduces the expression to its simplest form.

Variables and Coefficients

Understanding variables (letters representing numbers) and coefficients (numerical factors multiplying variables) is essential. When distributing, multiply the coefficient outside the parentheses by each coefficient inside, keeping the variable part unchanged.