Question

Which expression is the same as \(-6(8+3)\) ? A. \(-48-18\) B. \(-48+18\) C. \(48-18\) D. \(48+18\)

Short answer

A. \[-48 - 18.\]

Step-by-step solution

Distribute the Multiplication

Use the distributive property to simplify the expression \[-6(8+3)\]. This means multiplying \-6\ by each term inside the parentheses: \[-6 \times 8\] and \[-6 \times 3.\]

Multiply Each Term

\[-6 \times 8 = -48\] and \[-6 \times 3 = -18.\] Now, combine these results to get \[-48 + (-18).\]

Combine the Results

Simplify \[-48 + (-18)\] to get \[-48 - 18.\]

Identify the Matching Expression

Match \[-48 - 18\] with the given options. The answer is A. \[-48 - 18.\]

Key concepts

Simplifying Expressions

Simplifying expressions is a crucial skill in algebra. It involves reducing an algebraic expression to its simplest form. When simplifying an expression, we look for ways to combine like terms or use mathematical properties, such as the distributive property.

In the given exercise, we need to simplify the expression \(-6(8+3)\). By applying simplification techniques, we can make complex expressions easier to understand and solve.

For example, an expression like \(-6(8+3)\) looks complicated at first. But by breaking it down and using the distributive property, we simplify it and find the solution.

Multiplication

Multiplication is one of the basic operations in math and is essential for simplifying expressions. It involves finding the product of two numbers or terms.

In the original exercise, we use multiplication when we distribute \(-6\) to both \(8\) and \(3\). This process is called distributing or applying the distributive property. The steps involved include multiplying \(-6\) by \(8\) and \(-6\) by \(3\).

Here are the detailed steps:

• First, multiply \(-6 \times 8\) which equals \(-48\).
• Second, multiply \(-6 \times 3\) which equals \(-18\).
• Finally, combine these results: \(-48 - 18\)

This results in \(-66\), and it matches option A in the exercise. By understanding multiplication, we make it easier to solve and simplify expressions.

Combining Like Terms

Combining like terms is another essential step in simplifying expressions. Like terms are terms that have the same variable raised to the same power. Combining them helps to simplify expressions more efficiently.

In the current problem, combining like terms comes into play after we distribute the multiplication. We combined \(-48\) and \(-18\) since both terms are numbers.

Combining these terms involves simple addition: \(-48 + (-18) \):

• Add the two numbers: \(-48 - 18\) equals \(-66\).
• You can see that this step simplified the expression even further.

Combining like terms keeps expressions organized and easy to work with. This final step in solving the exercise led us to our answer.

By mastering this concept, you can tackle more complex algebraic problems with greater ease.