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Chapter 6: Problem 176

Multiply. $$-5(p+9)$$

Short Answer

Expert verified
-5p - 45

Step by step solution

01

Distribute the Constant

To multiply the expression -5(p + 9), distribute the -5 to each term inside the parentheses. This means you will multiply -5 by each term separately.
02

Multiply -5 by p

First, multiply -5 by p. The result of this is -5p.
03

Multiply -5 by 9

Next, multiply -5 by 9. The result of this is -45.
04

Combine the Results

Combine the terms from Steps 2 and 3 to get the final expression. So, the expression -5(p + 9) becomes -5p - 45.

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Key Concepts

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

Distributive Property
When you see a term outside of parentheses, like \(-5(p + 9)\), you will need to use the distributive property to simplify it. The distributive property helps you multiply a single term with two or more terms inside the parentheses.
In this exercise, \(-5\) is distributed to both \(p\) and \(9\). This means you perform the multiplication separately for each part inside the parentheses.
Here's what happens:
\[ -5(p + 9) \] becomes \[ -5 \times p + -5 \times 9 \]
This process breaks down the expression into smaller, more manageable parts, making it easier to solve.
Multiplying Expressions
Multiplying an expression involves multiplying each term individually. For instance, consider the given exercise - \(-5(p + 9)\).
First, you have the multiplication of \(-5\) and \(p\):
\[ -5 \times p = -5p \]
Next, multiply \(-5\) by \(9\):
\[ -5 \times 9 = -45 \]
Breaking down these multiplications makes it easier to handle. By separating each multiplication step, you simplify the overall expression gradually.
Combining Like Terms
In algebra, combining like terms means adding or subtracting terms that have the same variables. It helps in simplifying expressions further.
After distributing and multiplying, you get two terms \(-5p\) and \(-45\). These terms are not 'like terms' because one contains variable \(p\) and the other does not.
Thus, you just place them together:
\[ -5p - 45 \]
This is your final simplified expression, showing the result of correctly applying the distributive property and multiplication concepts.
Remember:
-Like terms have the same variable or no variable at all.
-Always combine and present them in their simplest form.

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