Add Using A Vertical Format. Simplify Your Answer.$(x^2 + 9x) + (-9x^2 - 3x$\]\[$\square\$\]

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Understanding the Problem

When simplifying algebraic expressions, it's essential to combine like terms and apply the rules of arithmetic operations. In this article, we'll focus on simplifying the given expression: (x2+9x)+(−9x2−3x)(x^2 + 9x) + (-9x^2 - 3x).

Breaking Down the Expression

To simplify the expression, we need to break it down into smaller parts and combine like terms. Let's start by identifying the like terms in the given expression.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are:

  • x2x^2
  • 9x9x
  • −9x2-9x^2
  • −3x-3x

Combining Like Terms

Now that we've identified the like terms, let's combine them using the rules of arithmetic operations.

Combining x2x^2 Terms

The x2x^2 terms are x2x^2 and −9x2-9x^2. To combine these terms, we need to add their coefficients.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = x**2 + (-9*x**2)

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

-8*x**2

So, the combined x2x^2 term is −8x2-8x^2.

Combining xx Terms

The xx terms are 9x9x and −3x-3x. To combine these terms, we need to add their coefficients.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = 9*x + (-3*x)

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

6*x

So, the combined xx term is 6x6x.

Simplifying the Expression

Now that we've combined the like terms, let's simplify the expression by combining the results.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = -8*x**2 + 6*x

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

-8*x**2 + 6*x

So, the simplified expression is −8x2+6x-8x^2 + 6x.

Conclusion

In this article, we've simplified the given algebraic expression by combining like terms and applying the rules of arithmetic operations. We've used Python code to demonstrate the simplification process and obtained the final simplified expression.

Final Answer

The final answer is −8x2+6x\boxed{-8x^2 + 6x}.

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Understanding the Problem

When simplifying algebraic expressions, it's essential to combine like terms and apply the rules of arithmetic operations. In this article, we'll focus on simplifying the given expression: (x2+9x)+(−9x2−3x)(x^2 + 9x) + (-9x^2 - 3x).

Breaking Down the Expression

To simplify the expression, we need to break it down into smaller parts and combine like terms. Let's start by identifying the like terms in the given expression.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are:

  • x2x^2
  • 9x9x
  • −9x2-9x^2
  • −3x-3x

Combining Like Terms

Now that we've identified the like terms, let's combine them using the rules of arithmetic operations.

Combining x2x^2 Terms

The x2x^2 terms are x2x^2 and −9x2-9x^2. To combine these terms, we need to add their coefficients.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = x**2 + (-9*x**2)

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

-8*x**2

So, the combined x2x^2 term is −8x2-8x^2.

Combining xx Terms

The xx terms are 9x9x and −3x-3x. To combine these terms, we need to add their coefficients.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = 9*x + (-3*x)

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

6*x

So, the combined xx term is 6x6x.

Simplifying the Expression

Now that we've combined the like terms, let's simplify the expression by combining the results.

# Import necessary modules
import sympy as sp

# Define variables
x = sp.symbols('x')

# Define the expression
expr = -8*x**2 + 6*x

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

The output of the above code is:

-8*x**2 + 6*x

So, the simplified expression is −8x2+6x-8x^2 + 6x.

Q&A

Q: What are like terms?

A: 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 need to add their coefficients.

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

A: Combining like terms involves adding or subtracting terms with the same variable raised to the same power. Simplifying an expression involves combining like terms and applying the rules of arithmetic operations.

Q: Can I use a calculator to simplify algebraic expressions?

A: Yes, you can use a calculator to simplify algebraic expressions. However, it's essential to understand the underlying math concepts to ensure accurate results.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms left to combine. You can use a calculator or manually simplify the expression to check if it's simplified.

Conclusion

In this article, we've simplified the given algebraic expression by combining like terms and applying the rules of arithmetic operations. We've also answered some common questions related to simplifying algebraic expressions.

Final Answer

The final answer is −8x2+6x\boxed{-8x^2 + 6x}.