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Chapter 10: Problem 150

Multiply. $$-4(p+15)$$

Short Answer

Expert verified
The result is \(-4p - 60\).

Step by step solution

01

Apply the Distributive Property

The distributive property states that for any numbers or variables, \(a(b+c) = ab + ac\). In this problem, multiply \(-4\) with each term inside the parentheses.
02

Multiply \(-4\) by \(p\)

First, multiply \(-4\) by \(p\): \[ -4 \times p = -4p \]
03

Multiply \(-4\) by 15

Next, multiply \(-4\) by 15: \[ -4 \times 15 = -60 \]
04

Combine the Results

Combine the results of the two multiplications: \[ -4(p + 15) = -4p - 60 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplication in algebra
When working with algebraic expressions, multiplication is a crucial operation. It involves multiplying numbers, variables, or a combination of both. This is particularly important when you need to apply the distributive property. For instance, if you have the expression \(-4(p + 15)\), you need to distribute \-4\ to each term inside the parentheses.

First, let's break it down:

  • Multiply \-4\ by \p\: \[ -4 \times p = -4p \]
  • Multiply \-4\ by 15: \[ -4 \times 15 = -60 \]

By performing these individual multiplications, you can then combine the results:\[-4(p + 15) = -4p - 60\]

This shows how distributive property and multiplication operate together in algebra.
combining like terms
Once you have applied the distributive property and multiplication, the next crucial step is combining like terms. In algebra, 'like terms' are terms that have the same variables raised to the same power.

For example, if we have the expression \(-4p - 60\), we examine each term:
  • \-4p\ is a term with the variable \p\
  • \-60\ is a constant term (it has no variable)

Since these terms are different (one has a variable and one does not), there are no like terms to combine in this specific example. The expression \(-4p - 60\) is therefore already simplified since there are no further like terms to combine. It's important to always check for like terms to ensure you have the simplest form of an expression.
prealgebra
Prealgebra is the foundation upon which all higher-level mathematical concepts are built. In prealgebra, you learn to work with simple algebraic expressions and understand the basics of arithmetic operations.

Key topics in prealgebra include:
  • Understanding and applying the distributive property: \(a(b+c) = ab + ac\)
  • Performing basic operations with variables and constants
  • Combining like terms

For the expression \(-4(p + 15)\), knowing prealgebra helps you:

  • Recognize the use of the distributive property to break down the expression
  • Multiply both terms inside the parentheses by \-4\
  • Simplify the expression to get \(-4p - 60\)

Developing strong prealgebra skills is essential for succeeding in more complex algebraic problems.

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