Rewrite The Expression. Y = 2 ( X + 3 ) 2 − 9 Y = 2(x+3)^2 - 9 Y = 2 ( X + 3 ) 2 − 9

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Introduction

In mathematics, expressions are a fundamental concept that helps us represent relationships between variables. One of the most common expressions in algebra is the quadratic expression, which is in the form of $ax^2 + bx + c$. However, expressions can be rewritten in various forms to make them easier to understand and work with. In this article, we will focus on rewriting the expression $y = 2(x+3)^2 - 9$.

Understanding the Expression

The given expression is $y = 2(x+3)^2 - 9$. This expression can be broken down into three parts:

• The first part is the squared term, $(x+3)^2$.
• The second part is the coefficient of the squared term, which is 2.
• The third part is the constant term, which is -9.

Rewriting the Expression

To rewrite the expression, we can start by expanding the squared term using the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this case, $a = x$ and $b = 3$. Therefore, we can expand the squared term as follows:

$(x+3)^2 = x^2 + 2 \cdot x \cdot 3 + 3^2$ $(x+3)^2 = x^2 + 6x + 9$

Now, we can substitute this expanded form back into the original expression:

$y = 2(x^2 + 6x + 9) - 9$

Distributing the Coefficient

The next step is to distribute the coefficient 2 to each term inside the parentheses:

$y = 2x^2 + 2 \cdot 6x + 2 \cdot 9 - 9$ $y = 2x^2 + 12x + 18 - 9$

Simplifying the Expression

Finally, we can simplify the expression by combining like terms:

$y = 2x^2 + 12x + 9$

Conclusion

In this article, we have rewritten the expression $y = 2(x+3)^2 - 9$ by expanding the squared term, distributing the coefficient, and simplifying the expression. The rewritten expression is $y = 2x^2 + 12x + 9$. This form of the expression is easier to work with and can be used to solve various mathematical problems.

Example Use Cases

The rewritten expression $y = 2x^2 + 12x + 9$ can be used in various mathematical problems, such as:

• Finding the maximum or minimum value of a quadratic function.
• Solving a quadratic equation.
• Graphing a quadratic function.

Tips and Tricks

When rewriting an expression, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps and using the correct order of operations, you can rewrite expressions like $y = 2(x+3)^2 - 9$ with ease.

Common Mistakes to Avoid

When rewriting an expression, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not following the order of operations (PEMDAS).
• Not distributing the coefficient correctly.
• Not combining like terms correctly.

By avoiding these common mistakes, you can ensure that your rewritten expression is accurate and easy to work with.

Conclusion

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Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about rewriting the expression $y = 2(x+3)^2 - 9$.

Q: What is the first step in rewriting the expression $y = 2(x+3)^2 - 9$?

A: The first step in rewriting the expression $y = 2(x+3)^2 - 9$ is to expand the squared term using the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this case, $a = x$ and $b = 3$.

Q: How do I expand the squared term $(x+3)^2$?

A: To expand the squared term $(x+3)^2$, you can use the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this case, $a = x$ and $b = 3$. Therefore, we can expand the squared term as follows:

$(x+3)^2 = x^2 + 2 \cdot x \cdot 3 + 3^2$ $(x+3)^2 = x^2 + 6x + 9$

Q: What is the next step in rewriting the expression $y = 2(x+3)^2 - 9$?

A: The next step in rewriting the expression $y = 2(x+3)^2 - 9$ is to distribute the coefficient 2 to each term inside the parentheses.

Q: How do I distribute the coefficient 2 to each term inside the parentheses?

A: To distribute the coefficient 2 to each term inside the parentheses, you can multiply each term by 2:

$y = 2(x^2 + 6x + 9) - 9$ $y = 2x^2 + 2 \cdot 6x + 2 \cdot 9 - 9$ $y = 2x^2 + 12x + 18 - 9$

Q: What is the final step in rewriting the expression $y = 2(x+3)^2 - 9$?

A: The final step in rewriting the expression $y = 2(x+3)^2 - 9$ is to simplify the expression by combining like terms.

Q: How do I simplify the expression $y = 2x^2 + 12x + 18 - 9$?

A: To simplify the expression $y = 2x^2 + 12x + 18 - 9$, you can combine like terms:

$y = 2x^2 + 12x + 9$

Q: What are some common mistakes to avoid when rewriting the expression $y = 2(x+3)^2 - 9$?

A: Some common mistakes to avoid when rewriting the expression $y = 2(x+3)^2 - 9$ include:

• Not following the order of operations (PEMDAS).
• Not distributing the coefficient correctly.
• Not combining like terms correctly.

Q: How can I use the rewritten expression $y = 2x^2 + 12x + 9$ in real-world problems?

A: The rewritten expression $y = 2x^2 + 12x + 9$ can be used in various real-world problems, such as:

• Finding the maximum or minimum value of a quadratic function.
• Solving a quadratic equation.
• Graphing a quadratic function.

Conclusion

In conclusion, rewriting the expression $y = 2(x+3)^2 - 9$ is a straightforward process that involves expanding the squared term, distributing the coefficient, and simplifying the expression. By following the correct steps and using the correct order of operations, you can rewrite expressions like this one with ease. Whether you're a student or a professional, understanding how to rewrite expressions is an essential skill that can help you solve mathematical problems with confidence.