Simplify The Expression:${ 8.3y(2.7y + 5.1) }$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems more efficiently. It involves rewriting an expression in a simpler form, often by combining like terms or removing unnecessary components. In this article, we will focus on simplifying the given expression: $8.3y(2.7y + 5.1)$. We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is a product of two terms: $8.3y$ and $(2.7y + 5.1)$. To simplify this expression, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. In this case, we can apply the distributive property to expand the expression.

Applying the Distributive Property

To simplify the expression, we will apply the distributive property by multiplying each term in the first factor ($8.3y$) with each term in the second factor ($2.7y + 5.1$). This will result in a new expression with multiple terms.

8.3y(2.7y + 5.1) = 8.3y(2.7y) + 8.3y(5.1)

Multiplying the Terms

Now, we will multiply the terms in the expression. We will start by multiplying $8.3y$ with $2.7y$, and then multiply $8.3y$ with $5.1$.

8.3y(2.7y) = 22.41y^2
8.3y(5.1) = 42.33y

Combining the Terms

Now that we have multiplied the terms, we can combine them to form a single expression. We will add the two terms together to get the final simplified expression.

22.41y^2 + 42.33y

Final Simplified Expression

The final simplified expression is $22.41y^2 + 42.33y$. This expression is a quadratic expression, which is a polynomial of degree two. We can further simplify this expression by factoring out the greatest common factor (GCF), if any.

Factoring Out the GCF

In this case, there is no common factor that can be factored out from the expression. Therefore, the final simplified expression remains the same: $22.41y^2 + 42.33y$.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems more efficiently. In this article, we simplified the expression $8.3y(2.7y + 5.1)$ by applying the distributive property and multiplying the terms. We then combined the terms to form a single expression and factored out the GCF, if any. The final simplified expression is $22.41y^2 + 42.33y$. We hope this article has provided a clear explanation of the steps involved in simplifying expressions and has helped you understand the concept better.

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• Q: How do I simplify an expression? A: To simplify an expression, you need to apply the distributive property, multiply the terms, and combine them to form a single expression.
• Q: What is a quadratic expression? A: A quadratic expression is a polynomial of degree two, which is an expression of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

References

• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
  

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Introduction

In our previous article, we simplified the expression $8.3y(2.7y + 5.1)$ by applying the distributive property and multiplying the terms. We then combined the terms to form a single expression and factored out the GCF, if any. 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 mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to expand an expression by multiplying each term in the first factor with each term in the second factor.

Q: How do I simplify an expression?

A: To simplify an expression, you need to apply the distributive property, multiply the terms, and combine them to form a single expression. You can also factor out the greatest common factor (GCF) if any.

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial of degree two, which is an expression of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.

Q: How do I know if an expression can be simplified?

A: An expression can be simplified if it can be rewritten in a simpler form by applying the distributive property, multiplying the terms, and combining them to form a single expression.

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

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

• Not applying the distributive property correctly
• Not multiplying the terms correctly
• Not combining the terms correctly
• Not factoring out the GCF correctly

Q: How do I check if my simplified expression is correct?

A: To check if your simplified expression is correct, you can:

• Plug in some values for the variable and check if the expression evaluates to the correct value
• Use a calculator to evaluate the expression and check if it matches the simplified expression
• Compare your simplified expression with the original expression to check if it is equivalent

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions
• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Tips and Tricks

• Always apply the distributive property correctly to expand an expression
• Multiply the terms correctly to get the correct product
• Combine the terms correctly to get the correct sum
• Factor out the GCF correctly to simplify the expression
• Check your simplified expression by plugging in some values for the variable or using a calculator

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems more efficiently. In this article, we answered some frequently asked questions related to simplifying expressions and provided additional resources for further learning. We hope this article has provided a clear explanation of the steps involved in simplifying expressions and has helped you understand the concept better.

Frequently Asked Questions (FAQs)

• Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• Q: How do I simplify an expression? A: To simplify an expression, you need to apply the distributive property, multiply the terms, and combine them to form a single expression.
• Q: What is a quadratic expression? A: A quadratic expression is a polynomial of degree two, which is an expression of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.

Related Articles

• Simplify the Expression: $8.3y(2.7y + 5.1)$
• Introduction to Algebra
• Introduction to Calculus
• Introduction to Mathematics for Computer Science

References

• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Mathematics for Computer Science" by Eric Lehman and Tom Leighton