Multiply And Simplify The Expression: { (u+5)(u-6)$}$

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Introduction

In algebra, multiplying and simplifying expressions is a fundamental concept that helps us solve equations and manipulate mathematical expressions. In this article, we will focus on multiplying and simplifying the expression {(u+5)(u-6)$}$. We will break down the process into manageable steps and provide a clear explanation of each step.

Understanding the Expression

Before we start multiplying and simplifying the expression, let's take a closer look at it. The expression {(u+5)(u-6)$}$ consists of two binomials, {u+5$}$ and {u-6$}$. To multiply these binomials, we will use the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac.

Step 1: Multiply the First Binomial by the Second Binomial

To multiply the first binomial {u+5$}$ by the second binomial {u-6$}$, we will use the distributive property. We will multiply each term in the first binomial by each term in the second binomial.

{(u+5)(u-6) = u(u) + u(-6) + 5(u) + 5(-6)$

Step 2: Simplify the Expression

Now that we have multiplied the binomials, let's simplify the expression. We will combine like terms and eliminate any unnecessary parentheses.

[$u(u) + u(-6) + 5(u) + 5(-6) = u^2 - 6u + 5u - 30$

Step 3: Combine Like Terms

The next step is to combine like terms. We will add or subtract the coefficients of the same variables.

[$u^2 - 6u + 5u - 30 = u^2 - u - 30$

Conclusion

In conclusion, multiplying and simplifying the expression [(u+5)(u-6)\$} involves breaking down the process into manageable steps. We used the distributive property to multiply the binomials and then simplified the expression by combining like terms. The final simplified expression is {u^2 - u - 30$}$.

Tips and Tricks

Here are some tips and tricks to help you multiply and simplify algebraic expressions:

  • Use the distributive property to multiply binomials.
  • Combine like terms to simplify the expression.
  • Eliminate unnecessary parentheses to make the expression easier to read.
  • Check your work by plugging in values for the variables.

Real-World Applications

Multiplying and simplifying algebraic expressions has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In economics, we use algebraic expressions to model the behavior of markets. In computer science, we use algebraic expressions to write algorithms and solve problems.

Common Mistakes to Avoid

Here are some common mistakes to avoid when multiplying and simplifying algebraic expressions:

  • Failing to use the distributive property when multiplying binomials.
  • Not combining like terms to simplify the expression.
  • Leaving unnecessary parentheses in the expression.
  • Not checking your work by plugging in values for the variables.

Conclusion

Introduction

In our previous article, we discussed how to multiply and simplify algebraic expressions. In this article, we will provide a Q&A guide to help you understand the concept better. We will answer some common questions and provide examples to illustrate the concepts.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, a(b + c) = ab + ac. This means that we can multiply a single term by two or more terms inside parentheses.

Q: How do I multiply binomials using the distributive property?

A: To multiply binomials using the distributive property, we will multiply each term in the first binomial by each term in the second binomial. For example, to multiply {(u+5)(u-6)$}$, we will multiply each term in the first binomial by each term in the second binomial.

{(u+5)(u-6) = u(u) + u(-6) + 5(u) + 5(-6)$

Q: What is the difference between multiplying and simplifying algebraic expressions?

A: Multiplying algebraic expressions involves combining two or more expressions using the distributive property. Simplifying algebraic expressions involves combining like terms and eliminating unnecessary parentheses.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, we will combine like terms and eliminate unnecessary parentheses. For example, to simplify the expression [u^2 - 6u + 5u - 30\$}, we will combine like terms.

{u^2 - 6u + 5u - 30 = u^2 - u - 30$

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

A: Some common mistakes to avoid when multiplying and simplifying algebraic expressions include:

  • Failing to use the distributive property when multiplying binomials.
  • Not combining like terms to simplify the expression.
  • Leaving unnecessary parentheses in the expression.
  • Not checking your work by plugging in values for the variables.

Q: How do I check my work when multiplying and simplifying algebraic expressions?

A: To check your work when multiplying and simplifying algebraic expressions, we will plug in values for the variables and evaluate the expression. For example, to check the expression [u^2 - u - 30\$}, we will plug in a value for u, such as u = 1.

{(1)^2 - (1) - 30 = 1 - 1 - 30 = -30$

Q: What are some real-world applications of multiplying and simplifying algebraic expressions?

A: Some real-world applications of multiplying and simplifying algebraic expressions include:

  • Physics: Algebraic expressions are used to describe the motion of objects.
  • Economics: Algebraic expressions are used to model the behavior of markets.
  • Computer Science: Algebraic expressions are used to write algorithms and solve problems.

Conclusion

In conclusion, multiplying and simplifying algebraic expressions is a fundamental concept in mathematics. By following the steps outlined in this article, you can multiply and simplify expressions with ease. Remember to use the distributive property, combine like terms, and eliminate unnecessary parentheses to simplify the expression. With practice and patience, you will become proficient in multiplying and simplifying algebraic expressions.

Additional Resources

For more information on multiplying and simplifying algebraic expressions, we recommend the following resources:

  • Khan Academy: Algebra
  • Mathway: Algebra
  • Wolfram Alpha: Algebra

Practice Problems

To practice multiplying and simplifying algebraic expressions, we recommend the following problems:

  • Multiply and simplify the expression [(x+2)(x-3)\$}.
  • Multiply and simplify the expression {(y-4)(y+5)$}$.
  • Simplify the expression {x^2 + 5x - 6x - 30$}$.

Answer Key

  • {(x+2)(x-3) = x^2 - 3x + 2x - 6 = x^2 - x - 6$
  • [$(y-4)(y+5) = y^2 + 5y - 4y - 20 = y^2 + y - 20$
  • [x^2 + 5x - 6x - 30 = x^2 - x - 30}