Simplify The Expression:${ 2d^2 + 3d + 4 + D - D^2 + 8 - D }$ { \square$}$ { D^2$}$ + { \square$}$ { D$}$ + { \square$}$

Introduction

In this article, we will simplify the given expression by combining like terms and rearranging the terms to make it easier to read and understand. The expression is given as:

${ 2d^2 + 3d + 4 + d - d^2 + 8 - d }$

Our goal is to simplify this expression and rewrite it in the standard form of a quadratic expression, which is:

${ ad^2 + bd + c }$

where a, b, and c are constants.

Step 1: Combine Like Terms

The first step in simplifying the expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have the following like terms:

• $2d^2$ and $-d^2$
• $3d$ and $d$ and $-d$
• $4$ and $8$

We can combine these like terms by adding or subtracting their coefficients.

Combining Like Terms: $2d^2$ and $-d^2$

When we combine $2d^2$ and $-d^2$, we get:

${ 2d^2 - d^2 = d^2 }$

So, the first term in the expression becomes $d^2$.

Combining Like Terms: $3d$ and $d$ and $-d$

When we combine $3d$ and $d$ and $-d$, we get:

${ 3d + d - d = 3d }$

So, the second term in the expression becomes $3d$.

Combining Like Terms: $4$ and $8$

When we combine $4$ and $8$, we get:

${ 4 + 8 = 12 }$

So, the third term in the expression becomes $12$.

Step 2: Rewrite the Expression

Now that we have combined like terms, we can rewrite the expression as:

${ d^2 + 3d + 12 }$

This is the simplified expression.

Step 3: Write the Expression in Standard Form

The standard form of a quadratic expression is:

${ ad^2 + bd + c }$

where a, b, and c are constants. In this case, we have:

• $a = 1$
• $b = 3$
• $c = 12$

So, the expression in standard form is:

${ d^2 + 3d + 12 }$

Conclusion

In this article, we simplified the given expression by combining like terms and rearranging the terms to make it easier to read and understand. We started with the expression:

${ 2d^2 + 3d + 4 + d - d^2 + 8 - d }$

and simplified it to:

${ d^2 + 3d + 12 }$

This is the simplified expression in standard form.

Final Answer

The final answer is:

${ d^2 + 3d + 12 }$

Discussion

This problem is a great example of how to simplify an expression by combining like terms and rearranging the terms. It is an important skill to have in algebra and is used frequently in solving equations and inequalities.

Related Problems

• Simplify the expression: $2x^2 + 3x + 4 + x - x^2 + 8 - x$
• Simplify the expression: $3y^2 + 2y + 5 + y - y^2 + 10 - y$
• Simplify the expression: $4z^2 + z + 6 + z - z^2 + 12 - z$

Introduction

In our previous article, we simplified the expression $2d^2 + 3d + 4 + d - d^2 + 8 - d$ by combining like terms and rearranging the terms to make it easier to read and understand. In this article, we will answer some frequently asked questions about simplifying expressions.

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to combine like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. For example, if you have $2x^2$ and $-x^2$, you can combine them by adding their coefficients:

$2x^2 - x^2 = x^2$

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is a step in simplifying an expression. Simplifying an expression involves combining like terms and rearranging the terms to make it easier to read and understand.

Q: How do I know if I have combined all the like terms?

A: To know if you have combined all the like terms, you need to check if there are any terms left that have the same variable raised to the same power. If there are, you need to combine them.

Q: Can I simplify an expression by rearranging the terms?

A: Yes, you can simplify an expression by rearranging the terms. However, this is not the same as combining like terms. Rearranging the terms involves changing the order of the terms, but not combining them.

Q: How do I write an expression in standard form?

A: To write an expression in standard form, you need to combine like terms and rearrange the terms to make it easier to read and understand. The standard form of a quadratic expression is:

$ad^2 + bd + c$

where a, b, and c are constants.

Q: What is the final answer to the expression $2d^2 + 3d + 4 + d - d^2 + 8 - d$?

A: The final answer to the expression $2d^2 + 3d + 4 + d - d^2 + 8 - d$ is:

$d^2 + 3d + 12$

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it is always a good idea to check your work by hand to make sure you have combined all the like terms.

Q: How do I know if I have simplified an expression correctly?

A: To know if you have simplified an expression correctly, you need to check if you have combined all the like terms and rearranged the terms to make it easier to read and understand.

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions. We covered topics such as combining like terms, rearranging terms, and writing expressions in standard form. We also provided examples and final answers to help illustrate the concepts.

Final Answer

The final answer is:

$d^2 + 3d + 12$

Discussion

This problem is a great example of how to simplify an expression by combining like terms and rearranging the terms. It is an important skill to have in algebra and is used frequently in solving equations and inequalities.

Related Problems

• Simplify the expression: $2x^2 + 3x + 4 + x - x^2 + 8 - x$
• Simplify the expression: $3y^2 + 2y + 5 + y - y^2 + 10 - y$
• Simplify the expression: $4z^2 + z + 6 + z - z^2 + 12 - z$

These problems are similar to the one we solved in this article and can be solved using the same techniques.