Simplify The Expression: $(3x - 5)^2$

by ADMIN 40 views

Introduction

In mathematics, simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. One of the most common types of expressions that need simplification is the square of a binomial. In this article, we will focus on simplifying the expression (3x−5)2(3x - 5)^2 using the formula for expanding a squared binomial.

Understanding the Formula

The formula for expanding a squared binomial is:

(a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2

where aa and bb are any real numbers. To simplify the expression (3x−5)2(3x - 5)^2, we can use this formula by substituting a=3xa = 3x and b=5b = 5.

Applying the Formula

Using the formula, we can expand the expression (3x−5)2(3x - 5)^2 as follows:

(3x−5)2=(3x)2−2(3x)(5)+52(3x - 5)^2 = (3x)^2 - 2(3x)(5) + 5^2

Simplifying the Expression

Now, we can simplify each term in the expression:

(3x)2=9x2(3x)^2 = 9x^2

2(3x)(5)=30x2(3x)(5) = 30x

52=255^2 = 25

Combining the Terms

Substituting the simplified terms back into the expression, we get:

(3x−5)2=9x2−30x+25(3x - 5)^2 = 9x^2 - 30x + 25

Conclusion

In this article, we have simplified the expression (3x−5)2(3x - 5)^2 using the formula for expanding a squared binomial. We have shown that the simplified expression is 9x2−30x+259x^2 - 30x + 25. This result can be used to solve equations and inequalities that involve this type of expression.

Real-World Applications

Simplifying algebraic expressions like (3x−5)2(3x - 5)^2 has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression (3x−5)2(3x - 5)^2 can be used to model the motion of an object under the influence of a force. In engineering, it can be used to design and optimize systems that involve quadratic equations.

Tips and Tricks

Here are some tips and tricks for simplifying expressions like (3x−5)2(3x - 5)^2:

  • Use the formula for expanding a squared binomial: The formula is a powerful tool for simplifying expressions like (3x−5)2(3x - 5)^2.
  • Substitute values carefully: When substituting values into the formula, make sure to use the correct values for aa and bb.
  • Simplify each term separately: Simplify each term in the expression separately before combining them.
  • Check your work: Always check your work to make sure that the simplified expression is correct.

Common Mistakes

Here are some common mistakes to avoid when simplifying expressions like (3x−5)2(3x - 5)^2:

  • Not using the formula: Failing to use the formula for expanding a squared binomial can lead to incorrect results.
  • Substituting incorrect values: Substituting incorrect values for aa and bb can lead to incorrect results.
  • Not simplifying each term separately: Failing to simplify each term separately can lead to incorrect results.
  • Not checking your work: Failing to check your work can lead to incorrect results.

Conclusion

In conclusion, simplifying the expression (3x−5)2(3x - 5)^2 using the formula for expanding a squared binomial is a crucial skill that has many real-world applications. By following the tips and tricks outlined in this article, you can simplify expressions like (3x−5)2(3x - 5)^2 with ease. Remember to always check your work to make sure that the simplified expression is correct.

Introduction

In our previous article, we simplified the expression (3x−5)2(3x - 5)^2 using the formula for expanding a squared binomial. In this article, we will answer some frequently asked questions about simplifying expressions like (3x−5)2(3x - 5)^2.

Q&A

Q: What is the formula for expanding a squared binomial?

A: The formula for expanding a squared binomial is:

(a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2

where aa and bb are any real numbers.

Q: How do I simplify the expression (3x−5)2(3x - 5)^2?

A: To simplify the expression (3x−5)2(3x - 5)^2, you can use the formula for expanding a squared binomial by substituting a=3xa = 3x and b=5b = 5. This will give you:

(3x−5)2=(3x)2−2(3x)(5)+52(3x - 5)^2 = (3x)^2 - 2(3x)(5) + 5^2

Q: What is the simplified expression for (3x−5)2(3x - 5)^2?

A: The simplified expression for (3x−5)2(3x - 5)^2 is:

(3x−5)2=9x2−30x+25(3x - 5)^2 = 9x^2 - 30x + 25

Q: Can I use the formula for expanding a squared binomial to simplify other expressions?

A: Yes, you can use the formula for expanding a squared binomial to simplify other expressions. For example, you can use it to simplify the expression (2x+3)2(2x + 3)^2 by substituting a=2xa = 2x and b=3b = 3.

Q: What are some common mistakes to avoid when simplifying expressions like (3x−5)2(3x - 5)^2?

A: Some common mistakes to avoid when simplifying expressions like (3x−5)2(3x - 5)^2 include:

  • Not using the formula for expanding a squared binomial
  • Substituting incorrect values for aa and bb
  • Not simplifying each term separately
  • Not checking your work

Q: How do I check my work when simplifying expressions like (3x−5)2(3x - 5)^2?

A: To check your work when simplifying expressions like (3x−5)2(3x - 5)^2, you can plug the simplified expression back into the original expression and see if it is true. For example, you can plug the simplified expression 9x2−30x+259x^2 - 30x + 25 back into the original expression (3x−5)2(3x - 5)^2 and see if it is equal to the original expression.

Q: What are some real-world applications of simplifying expressions like (3x−5)2(3x - 5)^2?

A: Simplifying expressions like (3x−5)2(3x - 5)^2 has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression (3x−5)2(3x - 5)^2 can be used to model the motion of an object under the influence of a force. In engineering, it can be used to design and optimize systems that involve quadratic equations.

Conclusion

In conclusion, simplifying expressions like (3x−5)2(3x - 5)^2 using the formula for expanding a squared binomial is a crucial skill that has many real-world applications. By following the tips and tricks outlined in this article, you can simplify expressions like (3x−5)2(3x - 5)^2 with ease. Remember to always check your work to make sure that the simplified expression is correct.

Additional Resources