(8x+9)*(8x-9) use The Suitable Identity To Get The Product

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Introduction

In algebra, the process of multiplying two binomials is a fundamental concept that is used extensively in various mathematical operations. The product of two binomials can be obtained using the distributive property, but it can also be simplified using the suitable identity. In this article, we will explore the process of multiplying the binomials (8x+9) and (8x-9) using the suitable identity.

The Suitable Identity

The suitable identity for multiplying two binomials is the difference of squares identity, which states that:

(a+b)(a-b) = a^2 - b^2

This identity can be used to simplify the product of two binomials by substituting the values of a and b.

Applying the Suitable Identity

To apply the suitable identity, we need to identify the values of a and b in the given binomials. In this case, we can see that the first binomial (8x+9) can be considered as (a+b) and the second binomial (8x-9) can be considered as (a-b).

Substituting the Values

Now, we can substitute the values of a and b into the difference of squares identity:

a = 8x b = 9

Substituting these values into the identity, we get:

(8x+9)(8x-9) = (8x)^2 - (9)^2

Simplifying the Expression

Now, we can simplify the expression by evaluating the squares:

(8x)^2 = 64x^2 (9)^2 = 81

Substituting these values into the expression, we get:

(8x+9)(8x-9) = 64x^2 - 81

Conclusion

In this article, we have seen how to multiply the binomials (8x+9) and (8x-9) using the suitable identity. By applying the difference of squares identity, we were able to simplify the product and obtain the final expression. This process demonstrates the importance of using the suitable identity in algebraic operations.

Example Problems

Here are a few example problems that demonstrate the use of the suitable identity:

  • (x+3)(x-3) = x^2 - 9
  • (2x+5)(2x-5) = 4x^2 - 25
  • (3x+2)(3x-2) = 9x^2 - 4

Tips and Tricks

Here are a few tips and tricks that can help you apply the suitable identity:

  • Make sure to identify the values of a and b in the given binomials.
  • Substitute the values of a and b into the difference of squares identity.
  • Simplify the expression by evaluating the squares.
  • Check your work by plugging in values for x.

Common Mistakes

Here are a few common mistakes that you should avoid when applying the suitable identity:

  • Failing to identify the values of a and b.
  • Substituting the wrong values into the identity.
  • Failing to simplify the expression.
  • Not checking your work.

Real-World Applications

The suitable identity has many real-world applications in fields such as physics, engineering, and economics. For example, it can be used to model the motion of objects, calculate the area of shapes, and analyze the behavior of financial systems.

Conclusion

In conclusion, the suitable identity is a powerful tool that can be used to simplify the product of two binomials. By applying the difference of squares identity, we can obtain the final expression and solve a wide range of algebraic problems. With practice and patience, you can master the use of the suitable identity and become proficient in algebraic operations.

Introduction

In our previous article, we explored the process of multiplying the binomials (8x+9) and (8x-9) using the suitable identity. In this article, we will answer some of the most frequently asked questions about the suitable identity and its application.

Q&A

Q: What is the suitable identity?

A: The suitable identity is the difference of squares identity, which states that:

(a+b)(a-b) = a^2 - b^2

This identity can be used to simplify the product of two binomials by substituting the values of a and b.

Q: How do I apply the suitable identity?

A: To apply the suitable identity, you need to identify the values of a and b in the given binomials. Then, substitute the values of a and b into the difference of squares identity and simplify the expression.

Q: What are some common mistakes to avoid when applying the suitable identity?

A: Some common mistakes to avoid when applying the suitable identity include:

  • Failing to identify the values of a and b.
  • Substituting the wrong values into the identity.
  • Failing to simplify the expression.
  • Not checking your work.

Q: Can I use the suitable identity to multiply any two binomials?

A: No, the suitable identity can only be used to multiply two binomials that are in the form (a+b) and (a-b). If the binomials are not in this form, you will need to use a different method to multiply them.

Q: How do I know if a binomial is in the form (a+b) or (a-b)?

A: To determine if a binomial is in the form (a+b) or (a-b), look for the signs of the terms. If the terms have the same sign, the binomial is in the form (a+b). If the terms have opposite signs, the binomial is in the form (a-b).

Q: Can I use the suitable identity to multiply more than two binomials?

A: No, the suitable identity can only be used to multiply two binomials. If you need to multiply more than two binomials, you will need to use a different method.

Q: How do I simplify the expression after applying the suitable identity?

A: To simplify the expression after applying the suitable identity, evaluate the squares and combine like terms.

Q: Can I use the suitable identity to solve real-world problems?

A: Yes, the suitable identity can be used to solve a wide range of real-world problems, including problems in physics, engineering, and economics.

Example Problems with Solutions

Here are a few example problems that demonstrate the use of the suitable identity:

  • (x+3)(x-3) = x^2 - 9
  • (2x+5)(2x-5) = 4x^2 - 25
  • (3x+2)(3x-2) = 9x^2 - 4

Tips and Tricks

Here are a few tips and tricks that can help you apply the suitable identity:

  • Make sure to identify the values of a and b in the given binomials.
  • Substitute the values of a and b into the difference of squares identity.
  • Simplify the expression by evaluating the squares.
  • Check your work by plugging in values for x.

Common Misconceptions

Here are a few common misconceptions about the suitable identity:

  • The suitable identity can only be used to multiply two binomials that are in the form (a+b) and (a-b).
  • The suitable identity can be used to multiply more than two binomials.
  • The suitable identity can be used to solve all types of algebraic problems.

Conclusion

In conclusion, the suitable identity is a powerful tool that can be used to simplify the product of two binomials. By applying the difference of squares identity, we can obtain the final expression and solve a wide range of algebraic problems. With practice and patience, you can master the use of the suitable identity and become proficient in algebraic operations.