Problem 25 Multiply. $$(3 x+4) x$$... [FREE SOLUTION]

Chapter 9: Problem 25

Multiply. $$(3 x+4) x$$

Short Answer

Expert verified

The solution to $(3x + 4) x$ is $3x^2 + 4x$.

Step by step solution

Distribute X to each term within the parentheses

First, we need to distribute $x$ to each term inside the parentheses. That is, $x$ should be multiplied with $3x$ and then with $4$.

Perform the multiplication

Multiplying $x$ by $3x$ results in $3x^2$, and multiplying $x$ by $4$ results in $4x$.

Combine the terms

Finally, we combine the two terms to get the final result: $3x^2 + 4x$.

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Key Concepts

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

Understanding the Distributive Property

The distributive property is a fundamental principle in algebra that allows us to simplify expressions by distributing, or spreading out, one operation across another. It's like distributing candies equally among friends from a bag.

In our exercise, we distribute the variable $x$ to each term inside the parentheses:

Multiply $x$ by $3x$
Multiply $x$ by $4$

This helps us simplify the expression by handling each part separately, making complex problems easier to solve. Always remember, when you see a term outside of parentheses, everything inside gets multiplied by that term.

Simplifying Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operations. In our task, $(3x + 4)$ is an example of an algebraic expression.

Here's what we did:

Break down the expression into manageable parts using the distributive property.
Multiply each part separately.

For instance, multiplying $x$ by $3x$ gives us $3x^2$. This way, we systematically reduce the complexity of the expression, one step at a time.

Combining Like Terms for Clarity

Combining like terms is akin to tidying up a room by grouping similar items together. It means merging terms in an expression that have the same variable raised to the same power.

In our example, after using the distributive property and simplifying, we have $3x^2 + 4x$.

Let's break this down:

$3x^2$ and $4x$ are different terms because their variables are raised to different powers ($x^2$ versus $x$).
Since they are not like terms, we cannot combine them further.

Combining like terms helps in reducing expressions to their simplest form, enhancing clarity and making it easier to solve or evaluate further.

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91影视

Multiply. $$(3 x+4) x$$

Short Answer

Step by step solution

Distribute X to each term within the parentheses

Perform the multiplication

Combine the terms

Key Concepts

Understanding the Distributive Property

Simplifying Algebraic Expressions

Combining Like Terms for Clarity

One App. One Place for Learning.

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