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Chapter 1: Problem 801

Simplify using the distributive property. $$ 16-3(y+8) $$

Short Answer

Expert verified
-3y - 8

Step by step solution

01

Identify the expression

Identify the expression that needs to be simplified: \(16 - 3(y + 8)\)
02

Apply the distributive property

Apply the distributive property by multiplying \(-3\) with both terms inside the parentheses: \( -3(y + 8) = -3y - 3 \times 8\)
03

Simplify the multiplication

Simplify \(-3 \times 8\) to get \(-24\). Now the expression is \(16 - 3y - 24\)
04

Combine like terms

Combine the constant terms \(16\) and \(-24\) to get \(-8\). So, the simplified expression is \(-3y - 8\)

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Key Concepts

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

Simplifying Expressions
When working with algebra, you often need to simplify expressions to make them easier to work with.
Simplifying involves rewriting the expression in a simpler form without changing its value.
In the given exercise, the expression to simplify is: \(16 - 3(y + 8)\).
To simplify such expressions, follow these steps:
  • First, use the distributive property to get rid of the parentheses.
  • Next, combine any like terms.

Let's go through each step in detail and understand it fully.
Combining Like Terms
To simplify an expression, one of the crucial steps is combining like terms.
Like terms are terms that have the same variable raised to the same power.
In the example \(16 - 3(y + 8)\), after applying the distributive property, we got: \(16 - 3y - 24\).
Here, the like terms are the constants: \(16\) and \(-24\).
Combining like terms means adding or subtracting these constants together:
  • \(16 - 24 = -8\)

So, our simplified expression now is:
\(-3y - 8\)
Algebraic Manipulation
Algebraic manipulation involves performing operations to transform an algebraic expression into a desired form.
In our exercise, we performed algebraic manipulation by using the distributive property and combining like terms.
These are common techniques used in algebraic manipulation:
  • Distributive Property: \(a(b + c) = ab + ac\)
  • Combining like terms: adding or subtracting coefficients of the same variables.

In our specific problem, we transformed \((16 - 3(y + 8))\) into
\( -3y - 8\) by correctly applying the distributive property and combining the constants after simplification.
Understanding algebraic manipulation is key to mastering algebraic expressions and solving equations efficiently.

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