Consider the expression 4(8x+5). Complete the following descriptions of parts …

Mathematics Questions

Consider the expression 4(8x+5). Complete the following descriptions of parts of the expression: 1. The entire expression is the product of ____. 2. On its own, (8x+5) is a sum with ___. The choices are: – 2 factors – 3 factors – 2 terms – 3 terms

Short Answer

The expression 4(8x+5) consists of two factors: the number 4 and the binomial (8x+5). The binomial itself, composed of two terms (8x and 5), signifies a sum that results from multiplying these factors together.

Step-by-Step Solution

Step 1: Identify the Factors

The expression 4(8x+5) consists of two main components called factors. These factors are:

  • The number 4
  • The binomial (8x+5)

This signifies that the expression is a result of the multiplication of these two factors.

Step 2: Understand the Product Explanation

The expression is recognized as a product, which results from the multiplication of one factor by another. In this case, it shows that:

  • The number 4 is multiplied by the binomial (8x+5).
  • This multiplication indicates how the components combine to create the final expression.

This fundamental understanding of multiplication helps clarify how the expression operates.

Step 3: Analyze the Binomial Structure

Focusing on the binomial (8x+5), it is defined as a sum that contains two terms. These terms are:

  • 8x – a term that includes a variable multiplied by a coefficient
  • 5 – a constant term

Therefore, this binomial qualifies as having two distinct terms added together, which is essential to its structure.

Related Concepts

Factors

Components of an expression that are multiplied together to form a product

Product

The result of multiplying two or more factors

Binomial

A polynomial with exactly two distinct terms or components.

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