I Will Mark You Brainliest If It Is Right..which Binomial Is The Expansion Of A²b²+6abcd +9c²d²See The Image ​

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Understanding Binomial Expansion

Binomial expansion is a mathematical concept that involves the expansion of a binomial expression, which is an algebraic expression consisting of two terms. In this article, we will explore the binomial expansion of the given expression A²B² + 6ABCD + 9C²D².

The Given Expression

The given expression is A²B² + 6ABCD + 9C²D². This expression consists of three terms: A²B², 6ABCD, and 9C²D².

Identifying the Binomial

To identify the binomial, we need to look for a pattern in the given expression. A binomial typically has the form (a + b) or (a - b), where a and b are variables or constants.

The Binomial Expansion Formula

The binomial expansion formula is given by:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

Expanding the Given Expression

To expand the given expression, we need to look for a pattern that matches the binomial expansion formula. Let's try to rewrite the given expression in the form (a + b)².

A²B² + 6ABCD + 9C²D² = (AB)² + 6(AB)(CD) + 9(CD)²

Now, let's compare this with the binomial expansion formula:

(a + b)² = a² + 2ab + b²

In this case, a = AB and b = CD.

The Binomial

The binomial is (AB + CD)².

The Expanded Form

The expanded form of the binomial is:

(AB + CD)² = (AB)² + 2(AB)(CD) + (CD)²

= A²B² + 2ABCD + C²D²

Conclusion

In conclusion, the binomial expansion of the given expression A²B² + 6ABCD + 9C²D² is (AB + CD)². The expanded form of the binomial is A²B² + 2ABCD + C²D².

Key Takeaways

  • Binomial expansion is a mathematical concept that involves the expansion of a binomial expression.
  • The binomial expansion formula is given by (a + b)² = a² + 2ab + b².
  • To expand a binomial expression, we need to look for a pattern that matches the binomial expansion formula.
  • The binomial expansion of the given expression A²B² + 6ABCD + 9C²D² is (AB + CD)².

Frequently Asked Questions

Q: What is binomial expansion?

A: Binomial expansion is a mathematical concept that involves the expansion of a binomial expression.

Q: What is the binomial expansion formula?

A: The binomial expansion formula is given by (a + b)² = a² + 2ab + b².

Q: How do I expand a binomial expression?

A: To expand a binomial expression, we need to look for a pattern that matches the binomial expansion formula.

Q: What is the binomial expansion of the given expression A²B² + 6ABCD + 9C²D²?

A: The binomial expansion of the given expression A²B² + 6ABCD + 9C²D² is (AB + CD)².

Q: What is the expanded form of the binomial (AB + CD)²?

Understanding Binomial Expansion

Binomial expansion is a mathematical concept that involves the expansion of a binomial expression, which is an algebraic expression consisting of two terms. In this article, we will explore the binomial expansion of the given expression A²B² + 6ABCD + 9C²D².

The Binomial Expansion Formula

The binomial expansion formula is given by:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

Frequently Asked Questions

Q: What is binomial expansion?

A: Binomial expansion is a mathematical concept that involves the expansion of a binomial expression.

Q: What is the binomial expansion formula?

A: The binomial expansion formula is given by (a + b)² = a² + 2ab + b².

Q: How do I expand a binomial expression?

A: To expand a binomial expression, we need to look for a pattern that matches the binomial expansion formula.

Q: What is the binomial expansion of the given expression A²B² + 6ABCD + 9C²D²?

A: The binomial expansion of the given expression A²B² + 6ABCD + 9C²D² is (AB + CD)².

Q: What is the expanded form of the binomial (AB + CD)²?

A: The expanded form of the binomial (AB + CD)² is A²B² + 2ABCD + C²D².

Q: What is the difference between (a + b)² and (a - b)²?

A: The difference between (a + b)² and (a - b)² is the sign of the middle term. In (a + b)², the middle term is 2ab, while in (a - b)², the middle term is -2ab.

Q: How do I apply the binomial expansion formula to a binomial expression?

A: To apply the binomial expansion formula to a binomial expression, you need to identify the values of a and b, and then plug them into the formula.

Q: What are some common applications of binomial expansion?

A: Binomial expansion has many common applications in mathematics, science, and engineering, including the expansion of polynomials, the calculation of probabilities, and the solution of differential equations.

Q: Can I use binomial expansion to expand a trinomial expression?

A: No, binomial expansion is only applicable to binomial expressions, which consist of two terms. To expand a trinomial expression, you need to use a different method, such as the distributive property.

Q: How do I determine the degree of a binomial expression?

A: The degree of a binomial expression is the sum of the degrees of the two terms. For example, the degree of (a + b)² is 2, while the degree of (a + b)³ is 3.

Q: Can I use binomial expansion to expand a rational expression?

A: No, binomial expansion is only applicable to binomial expressions, which consist of two terms. To expand a rational expression, you need to use a different method, such as the distributive property.

Q: How do I apply binomial expansion to a real-world problem?

A: To apply binomial expansion to a real-world problem, you need to identify the binomial expression, determine the values of a and b, and then plug them into the formula. You can then use the expanded form to solve the problem.

Conclusion

In conclusion, binomial expansion is a powerful mathematical concept that has many applications in mathematics, science, and engineering. By understanding the binomial expansion formula and how to apply it, you can expand binomial expressions and solve a wide range of problems.

Key Takeaways

  • Binomial expansion is a mathematical concept that involves the expansion of a binomial expression.
  • The binomial expansion formula is given by (a + b)² = a² + 2ab + b².
  • To expand a binomial expression, you need to look for a pattern that matches the binomial expansion formula.
  • The binomial expansion of the given expression A²B² + 6ABCD + 9C²D² is (AB + CD)².
  • The expanded form of the binomial (AB + CD)² is A²B² + 2ABCD + C²D².

Additional Resources

  • Khan Academy: Binomial Expansion
  • Mathway: Binomial Expansion
  • Wolfram Alpha: Binomial Expansion

Practice Problems

  1. Expand the binomial expression (a + b)³.
  2. Expand the binomial expression (a - b)².
  3. Determine the degree of the binomial expression (a + b)².
  4. Apply binomial expansion to the real-world problem of calculating the probability of a coin toss.
  5. Expand the binomial expression (a + b)⁴.