Simplify The Expression: ( 2 + M ) ( 5 − M (2+m)(5-m ( 2 + M ) ( 5 − M ]

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical statements. The expression $(2+m)(5-m)$ is a quadratic expression that can be simplified using the distributive property and combining like terms. In this article, we will guide you through the step-by-step process of simplifying this expression.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. In the expression $(2+m)(5-m)$, we can apply the distributive property to expand the expression.

The Distributive Property Formula

The distributive property formula is:

$a(b+c) = ab + ac$

where $a$, $b$, and $c$ are algebraic expressions.

Applying the Distributive Property

Using the distributive property formula, we can expand the expression $(2+m)(5-m)$ as follows:

$(2+m)(5-m) = 2(5-m) + m(5-m)$

Expanding the Expression

Now that we have applied the distributive property, we can expand the expression further by multiplying each term inside the parentheses with the term outside the parentheses.

Expanding the First Term

The first term is $2(5-m)$. We can expand this term by multiplying $2$ with each term inside the parentheses:

$2(5-m) = 2(5) - 2(m)$

$2(5-m) = 10 - 2m$

Expanding the Second Term

The second term is $m(5-m)$. We can expand this term by multiplying $m$ with each term inside the parentheses:

$m(5-m) = m(5) - m(m)$

$m(5-m) = 5m - m^2$

Combining Like Terms

Now that we have expanded the expression, we can combine like terms to simplify it further.

Combining Like Terms Formula

The formula for combining like terms is:

$a + a = 2a$

$a + b = a + b$

where $a$ and $b$ are algebraic expressions.

Combining Like Terms

Using the combining like terms formula, we can combine the like terms in the expression:

$10 - 2m + 5m - m^2$

We can combine the like terms $-2m$ and $5m$ to get:

$10 + 3m - m^2$

Final Simplified Expression

The final simplified expression is:

$10 + 3m - m^2$

This is the simplified form of the original expression $(2+m)(5-m)$.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and manipulate mathematical statements. In this article, we have guided you through the step-by-step process of simplifying the expression $(2+m)(5-m)$ using the distributive property and combining like terms. By following these steps, you can simplify any quadratic expression and solve equations with confidence.

Frequently Asked Questions

• What is the distributive property? The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
• How do I apply the distributive property? To apply the distributive property, you can use the formula $a(b+c) = ab + ac$ and multiply each term inside the parentheses with the term outside the parentheses.
• What is the formula for combining like terms? The formula for combining like terms is $a + a = 2a$ and $a + b = a + b$, where $a$ and $b$ are algebraic expressions.

Additional Resources

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Quadratic Expressions: A Step-by-Step Guide
• Distributive Property: A Visual Guide
  

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Introduction

In our previous article, we guided you through the step-by-step process of simplifying the expression $(2+m)(5-m)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional resources for further learning.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you can use the formula $a(b+c) = ab + ac$ and multiply each term inside the parentheses with the term outside the parentheses.

Q: What is the formula for combining like terms?

A: The formula for combining like terms is $a + a = 2a$ and $a + b = a + b$, where $a$ and $b$ are algebraic expressions.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you can use the distributive property to expand the expression and then combine like terms.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression with one variable and a degree of 1, while a quadratic expression is an expression with one variable and a degree of 2.

Q: How do I determine the degree of an expression?

A: To determine the degree of an expression, you can count the number of variables and the number of exponents. The degree of an expression is the sum of the exponents.

Q: What is the importance of simplifying expressions?

A: Simplifying expressions is an essential skill in algebra that helps us solve equations and manipulate mathematical statements. By simplifying expressions, we can make it easier to solve equations and understand the relationships between variables.

Q: How do I know when to use the distributive property?

A: You can use the distributive property when you have an expression with parentheses and you want to expand it.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not using the distributive property when necessary
• Not combining like terms
• Not checking for errors in the expression

Additional Resources

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Quadratic Expressions: A Step-by-Step Guide
• Distributive Property: A Visual Guide
• Linear and Quadratic Expressions: A Comparison
• Algebraic Manipulation: A Guide to Simplifying Expressions

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and manipulate mathematical statements. By understanding the distributive property and combining like terms, we can simplify expressions and make it easier to solve equations. In this article, we have answered some frequently asked questions related to simplifying expressions and provided additional resources for further learning.

Frequently Asked Questions (FAQs)

• What is the distributive property?
• How do I apply the distributive property?
• What is the formula for combining like terms?
• How do I simplify a quadratic expression?
• What is the difference between a linear expression and a quadratic expression?
• How do I determine the degree of an expression?
• What is the importance of simplifying expressions?
• How do I know when to use the distributive property?
• What are some common mistakes to avoid when simplifying expressions?

Related Articles

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Quadratic Expressions: A Step-by-Step Guide
• Distributive Property: A Visual Guide
• Linear and Quadratic Expressions: A Comparison
• Algebraic Manipulation: A Guide to Simplifying Expressions

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