Problem 69 Rewrite each expression using th... [FREE SOLUTION]

Chapter 1: Problem 69

Rewrite each expression using the distributive property. Simplify if possible. $$10(m+5 n-3)$$

Short Answer

Expert verified

The simplified expression after applying the distributive property is $10m + 50n - 30$.

Step by step solution

Distribute the 10

Multiply 10 with each term inside the parentheses: $10 \times m + 10 \times 5n - 10 \times 3$. It becomes $10m + 50n - 30$.

Final Expression

So, the simplified expression after applying the distributive property is $10m + 50n - 30$.

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Key Concepts

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

Algebra Expressions

Algebra expressions are combinations of symbols and numbers created by using different operations like addition, subtraction, multiplication, and division. They often include variables, which are symbols that stand for numbers, and coefficients, which are numbers that multiply a variable. In an expression like $10(m+5n-3)$, each part has a role. Here, 10 is a coefficient, $m$ and $n$ are variables, and the terms within the parentheses $+5n$ and $-3$ modify $m$ and $n$.

Variables: Represent unknown values.
Coefficients: Numbers multiplying the variables (e.g., 10).
Constants: Numbers without variables (e.g., -3).

Understanding how these pieces fit together is crucial for evaluating and simplifying algebraic expressions using various algebraic properties.

Simplifying Expressions

Simplifying an algebraic expression means rewriting it in a form that is easier to work with or understand. Often, this involves combining like terms and using mathematical properties, such as the distributive property, to rearrange the expression. In the given expression $10(m+5n-3)$, the aim is to make it as straightforward as possible after applying algebraic operations.

First, apply the distributive property.
Rewrite each part separately, combining any similar terms.

Once the expression $10m + 50n - 30$ is formed, it is the simplest form of the given expression. Simplifying is important as it makes equations easier to solve, providing clarity to the solution process.

Multiplication in Algebra

Multiplication in algebra involves multiplying coefficients with variables or other numbers to expand expressions. The distributive property is a key multiplication method where you multiply each term inside a set of parentheses by a factor outside. With the expression $10(m+5n-3)$, the number 10 is multiplied by each term within the parentheses. It changes into three separate multiplications.

$10 \times m = 10m$
$10 \times 5n = 50n$
$10 \times (-3) = -30$

Using multiplication helps in transforming and simplifying expressions, creating a clearer path for further mathematical operations or problem-solving.

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91影视

Rewrite each expression using the distributive property. Simplify if possible. $$10(m+5 n-3)$$

Short Answer

Step by step solution

Distribute the 10

Final Expression

Key Concepts

Algebra Expressions

Simplifying Expressions

Multiplication in Algebra

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