Simplify.\[$-9u^2 - 11u^2\$\]

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Understanding the Problem

When dealing with algebraic expressions, simplification is a crucial step in solving equations and manipulating variables. In this case, we are given an expression that involves the combination of two like terms, −9u2-9u^2 and −11u2-11u^2. Our goal is to simplify this expression by combining like terms.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this case, both terms have the variable uu raised to the power of 2. To combine like terms, we add or subtract their coefficients. The coefficient of a term is the numerical value that multiplies the variable.

Simplifying the Expression

To simplify the expression −9u2−11u2-9u^2 - 11u^2, we need to combine the two like terms. We add the coefficients of the two terms, which are -9 and -11.

# Define the coefficients of the two terms
coefficient1 = -9
coefficient2 = -11

# Combine the coefficients
combined_coefficient = coefficient1 + coefficient2

Calculating the Combined Coefficient

When we add the coefficients -9 and -11, we get:

# Calculate the combined coefficient
combined_coefficient = -9 + (-11)
print(combined_coefficient)

Output

The output of the code is:

-20

Simplified Expression

Now that we have calculated the combined coefficient, we can simplify the expression by replacing the two like terms with their combined coefficient.

Final Answer

The simplified expression is:

−20u2-20u^2

Conclusion

In this article, we simplified the expression −9u2−11u2-9u^2 - 11u^2 by combining like terms. We added the coefficients of the two terms and replaced the original expression with the combined coefficient. This process is an essential step in solving equations and manipulating variables in algebra.

Additional Tips and Tricks

  • When combining like terms, make sure to add or subtract their coefficients.
  • Use the distributive property to simplify expressions with multiple terms.
  • Practice simplifying expressions with different variables and coefficients to become more comfortable with the process.

Common Mistakes to Avoid

  • Failing to identify like terms and combine them correctly.
  • Adding or subtracting coefficients incorrectly.
  • Not using the distributive property to simplify expressions with multiple terms.

Real-World Applications

Simplifying expressions is a crucial step in solving equations and manipulating variables in various fields, including:

  • Physics: Simplifying expressions is essential in solving equations that describe the motion of objects.
  • Engineering: Simplifying expressions is necessary in designing and analyzing complex systems.
  • Economics: Simplifying expressions is used in modeling economic systems and making predictions about future trends.

Final Thoughts

Simplifying expressions is a fundamental concept in algebra that has numerous real-world applications. By understanding how to combine like terms and simplify expressions, you can solve equations and manipulate variables with ease. Practice simplifying expressions with different variables and coefficients to become more comfortable with the process.

Frequently Asked Questions

  • Q: What is the difference between like terms and unlike terms? A: Like terms are terms that have the same variable raised to the same power, while unlike terms are terms that have different variables or powers.
  • Q: How do I combine like terms? A: To combine like terms, add or subtract their coefficients.
  • Q: What is the distributive property? A: The distributive property is a rule that allows us to simplify expressions with multiple terms by multiplying each term by a coefficient.

References

Related Topics

Glossary

  • Like Terms: Terms that have the same variable raised to the same power.
  • Unlike Terms: Terms that have different variables or powers.
  • Coefficient: The numerical value that multiplies the variable.
  • Distributive Property: A rule that allows us to simplify expressions with multiple terms by multiplying each term by a coefficient.

Frequently Asked Questions

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power, while unlike terms are terms that have different variables or powers.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients.

Q: What is the distributive property?

A: The distributive property is a rule that allows us to simplify expressions with multiple terms by multiplying each term by a coefficient.

Q: Can I simplify an expression with variables and constants?

A: Yes, you can simplify an expression with variables and constants by combining like terms and using the distributive property.

Q: How do I know if two terms are like terms?

A: Two terms are like terms if they have the same variable raised to the same power.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients by combining like terms and using the distributive property.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, combine like terms and use the distributive property.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions by combining like terms and using the distributive property.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, combine like terms and use the distributive property.

Q: Can I simplify an expression with radicals?

A: Yes, you can simplify an expression with radicals by combining like terms and using the distributive property.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, combine like terms and use the distributive property.

Q: Can I simplify an expression with inequalities?

A: Yes, you can simplify an expression with inequalities by combining like terms and using the distributive property.

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, follow the order of operations (PEMDAS) and combine like terms.

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses by combining like terms and using the distributive property.

Q: How do I simplify an expression with exponents and fractions?

A: To simplify an expression with exponents and fractions, combine like terms and use the distributive property.

Q: Can I simplify an expression with radicals and fractions?

A: Yes, you can simplify an expression with radicals and fractions by combining like terms and using the distributive property.

Q: How do I simplify an expression with multiple variables and exponents?

A: To simplify an expression with multiple variables and exponents, combine like terms and use the distributive property.

Q: Can I simplify an expression with absolute values and fractions?

A: Yes, you can simplify an expression with absolute values and fractions by combining like terms and using the distributive property.

Q: How do I simplify an expression with inequalities and fractions?

A: To simplify an expression with inequalities and fractions, combine like terms and use the distributive property.

Q: Can I simplify an expression with multiple operations and fractions?

A: Yes, you can simplify an expression with multiple operations and fractions by combining like terms and using the distributive property.

Additional Resources

Related Topics

Glossary

  • Like Terms: Terms that have the same variable raised to the same power.
  • Unlike Terms: Terms that have different variables or powers.
  • Coefficient: The numerical value that multiplies the variable.
  • Distributive Property: A rule that allows us to simplify expressions with multiple terms by multiplying each term by a coefficient.