Problem 63 - Algebra 1

Question

Apply the distributive property. $$-2(d-5)$$

Step-by-Step Solution

Answer

-2d +10

Step 1: Distribute -2 to 'd'

Multiply -2 with d, which gives -2d. This is the first part of the expression.

Step 2: Distribute -2 to '-5'

Multiply -2 with -5, which gives 10. Remember when a negative number is multiplied by a negative number, the result is positive. This forms the second part of the expression.

Step 3: Combine Both Parts

Now, combine the two parts of the expression obtained from the previous steps to get the final answer -2d + 10.

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations. It involves finding the product of two numbers. To understand multiplication, think of it as repeated addition. For example, multiplying 3 by 4 is the same as adding 3 four times: 3 + 3 + 3 + 3.

In mathematics, multiplication follows certain rules and properties, like the commutative and distributive properties. The distributive property is especially useful when dealing with multiplication in algebraic expressions. It allows you to simplify expressions by multiplying each term inside a bracket by the term outside. This property is what we used in our exercise to simplify \(-2(d-5)\). When applying the distributive property, we multiply each term inside the bracket by \(-2\), hence, \(-2d\) and \(-2 imes -5 = 10\).

• Multiply terms in steps for clarity.
• Follow the multiplication rules, like sign rules.
• Simplify if possible after multiplying.
  

Negative Numbers

Negative numbers are numbers less than zero. They are usually denoted with a minus sign. When working with negative numbers, it is important to understand how they interact with other numbers, especially during multiplication.

Here is a simple rule: multiplying two negative numbers gives a positive product. This is because the two negatives "cancel out" each other. However, when a negative number is multiplied by a positive number, the result is negative. For example:

• \(-2 imes -3 = 6\) (positive result)
• \(-2 imes 3 = -6\) (negative result)

In our exercise, multiplying \(-2\) by \(-5\) provides a positive result of 10. Understanding these rules can help reduce errors during calculations and simplify algebraic expressions.

Keep these rules in mind when you process algebraic expressions; they will guide you to the right answers.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. Unlike regular numbers, algebraic expressions can include unknown numbers, represented as variables like \(d\) in our exercise.

Working with algebraic expressions involves a few key operations: simplifying, evaluating, and solving them. The goal of simplifying expressions, as in our exercise, is to make them as short and clear as possible without changing their value.

• Use the distributive property to remove parentheses.
• Combine like terms to simplify expressions.
• Keep track of variable and constant terms.

In our example, the expression \(-2(d-5)\) was simplified using the distributive property to become \(-2d + 10\). Here, \(-2d\) is the variable term and 10 is the constant term.

Understanding these components will help you handle more complex algebraic problems in the future.