Simplify The Expression: { (-5d + 1)(-2)$}$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps in solving equations and inequalities. It involves combining like terms, removing parentheses, and performing operations to make the expression more manageable. In this article, we will focus on simplifying the given expression: {(-5d + 1)(-2)$}$. We will use the distributive property and other algebraic techniques to simplify the 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. In the given expression, we have two sets of parentheses: (−5d+1){(-5d + 1)} and (−2){(-2)}. To simplify the expression, we will use the distributive property to multiply each term inside the first set of parentheses with the term outside.

Applying the Distributive Property

To apply the distributive property, we will multiply each term inside the first set of parentheses with the term outside. This means we will multiply (−5d){(-5d)} and (−2){(-2)}, and then multiply (1){(1)} and (−2){(-2)}.

(−5d+1)(−2)=(−5d)(−2)+(1)(−2){ (-5d + 1)(-2) = (-5d)(-2) + (1)(-2) }

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression by performing the multiplication operations.

(−5d)(−2)=10d{ (-5d)(-2) = 10d }

(1)(−2)=−2{ (1)(-2) = -2 }

Combining Like Terms

We can now combine the two simplified expressions to get the final result.

10d−2{ 10d - 2 }

Conclusion

In this article, we simplified the given expression: {(-5d + 1)(-2)$}$ using the distributive property and other algebraic techniques. We applied the distributive property to multiply each term inside the first set of parentheses with the term outside, and then simplified the expression by performing the multiplication operations. Finally, we combined like terms to get the final result. This example demonstrates the importance of simplifying expressions in mathematics and how it can be achieved using various algebraic techniques.

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.
  • How do I apply the distributive property? To apply the distributive property, multiply each term inside the first set of parentheses with the term outside.
  • What is the final result of the given expression? The final result of the given expression is 10d−2{10d - 2}.

Tips and Tricks

  • Use the distributive property to simplify expressions: The distributive property is a powerful tool that can be used to simplify expressions by multiplying each term inside the parentheses with the term outside.
  • Combine like terms: After applying the distributive property, combine like terms to get the final result.
  • Practice, practice, practice: Simplifying expressions is a skill that requires practice to develop. Try simplifying different expressions to become more comfortable with the process.

Further Reading

  • Algebraic Expressions: Learn more about algebraic expressions and how to simplify them using various techniques.
  • Distributive Property: Explore the distributive property in more detail and learn how to apply it to different types of expressions.
  • Simplifying Expressions: Discover more tips and tricks for simplifying expressions and become a master of algebraic manipulation.

Introduction

In our previous article, we simplified the expression: {(-5d + 1)(-2)$}$ using the distributive property and other algebraic techniques. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional tips and tricks for mastering algebraic manipulation.

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.

Q: How do I apply the distributive property?

A: To apply the distributive property, multiply each term inside the first set of parentheses with the term outside.

Q: What is the final result of the given expression?

A: The final result of the given expression is 10d−2{10d - 2}.

Q: Can I simplify expressions with multiple sets of parentheses?

A: Yes, you can simplify expressions with multiple sets of parentheses by applying the distributive property multiple times.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms with the same variable.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable, while a variable is a letter or symbol that represents a value.

Q: Can I simplify expressions with negative coefficients?

A: Yes, you can simplify expressions with negative coefficients by following the same rules as positive coefficients.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, multiply the numerator and denominator by the same value to eliminate the fraction.

Q: Can I simplify expressions with exponents?

A: Yes, you can simplify expressions with exponents by following the rules of exponentiation.

Tips and Tricks

  • Use the distributive property to simplify expressions: The distributive property is a powerful tool that can be used to simplify expressions by multiplying each term inside the parentheses with the term outside.
  • Combine like terms: After applying the distributive property, combine like terms to get the final result.
  • Practice, practice, practice: Simplifying expressions is a skill that requires practice to develop. Try simplifying different expressions to become more comfortable with the process.
  • Use algebraic properties to simplify expressions: Algebraic properties such as the commutative, associative, and distributive properties can be used to simplify expressions.
  • Simplify expressions step by step: Break down complex expressions into smaller parts and simplify each part step by step.

Common Mistakes to Avoid

  • Not applying the distributive property: Failing to apply the distributive property can lead to incorrect simplification of expressions.
  • Not combining like terms: Failing to combine like terms can lead to incorrect simplification of expressions.
  • Not following the order of operations: Failing to follow the order of operations (PEMDAS) can lead to incorrect simplification of expressions.

Further Reading

  • Algebraic Expressions: Learn more about algebraic expressions and how to simplify them using various techniques.
  • Distributive Property: Explore the distributive property in more detail and learn how to apply it to different types of expressions.
  • Simplifying Expressions: Discover more tips and tricks for simplifying expressions and become a master of algebraic manipulation.

Conclusion

Simplifying expressions is a crucial skill in mathematics that requires practice and patience to develop. By following the tips and tricks outlined in this article, you can become more comfortable with simplifying expressions and master algebraic manipulation. Remember to use the distributive property, combine like terms, and practice, practice, practice to become a master of simplifying expressions.