Verified Answer :

  • Identify the expression as a multiplication of a scalar by a binomial.
  • Use the distributive property \(a(b + c) = ab + ac\) to expand the expression.
  • Multiply \(-3\) by \(2x\) to get \(-6x\).
  • Multiply \(-3\) by \(4\) to get \(-12\), resulting in the final expression \(\boxed{-6x - 12}\).

Explanation

  1. Analyzing the Expression

To simplify the expression \(-3(2x + 4)\), we need to apply the distributive property of multiplication. The distributive property states that for any real numbers \(a, b,\) and \(c\), the expression \(a(b + c)\) is equivalent to \(ab + ac\). In our case, \(a = -3\), \(b = 2x\), and \(c = 4\).

  1. Applying the Distributive Property

Applying the distributive property, we multiply \(-3\) by each term inside the parentheses:
\[-3(2x + 4) = (-3 \times 2x) + (-3 \times 4)\]
Calculating each part individually:

  • First, multiply \(-3\) by \(2x\), which gives \(-6x\).
  • Next, multiply \(-3\) by \(4\), which gives \(-12\).

Combining these results, we get the simplified expression: \(-6x - 12\).

Examples

The distributive property is a fundamental tool in algebra, useful for simplifying complex expressions and solving equations. Imagine you are managing an inventory where you have 3 boxes, each containing 2 units of product X and 4 units of product Y. To find the total inventory, you calculate 3 times the sum of X and Y, expressed as \(3(2x + 4y)\). By distributing the 3, you find you have \(6x + 12y\) total items. This helps in organizing, budgeting, and planning logistics efficiently.

Related Questions