Simplify The Expression $(2a - 3b)^2$.

$$

Introduction

In algebra, simplifying expressions is a crucial skill that helps in solving equations and manipulating mathematical statements. 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 $(2a - 3b)^2$ using the formula for expanding a squared binomial.

Understanding the Formula for Expanding a Squared Binomial

The formula for expanding a squared binomial is given by:

$$(a + b)^2 = a^2 + 2ab + b^2$$

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

This formula can be used to expand any squared binomial, and it is a fundamental concept in algebra.

Applying the Formula to Simplify the Expression

To simplify the expression $(2a - 3b)^2$, we can use the formula for expanding a squared binomial. We will treat $2a$ as the first term and $-3b$ as the second term.

Using the formula for expanding a squared binomial, we get:

$$(2a - 3b)^2 = (2a)^2 - 2(2a)(3b) + (-3b)^2$$

Expanding the Terms

Now, let's expand the terms in the expression:

$$(2a)^2 = 4a^2$$

$$-2(2a)(3b) = -12ab$$

$$(-3b)^2 = 9b^2$$

Combining the Terms

Now, let's combine the terms in the expression:

$$(2a - 3b)^2 = 4a^2 - 12ab + 9b^2$$

Simplifying the Expression

The expression $4a^2 - 12ab + 9b^2$ can be simplified further by factoring out the greatest common factor (GCF) of the terms. In this case, the GCF is 1, so the expression cannot be simplified further.

Conclusion

In conclusion, the expression $(2a - 3b)^2$ can be simplified using the formula for expanding a squared binomial. By applying the formula and expanding the terms, we get the simplified expression $4a^2 - 12ab + 9b^2$. This expression cannot be simplified further, and it is the final simplified form of the original expression.

Final Answer

The final answer is $\boxed{4a^2 - 12ab + 9b^2}$.

Additional Tips and Tricks

• When simplifying expressions, always look for the greatest common factor (GCF) of the terms.
• Use the formula for expanding a squared binomial to simplify expressions of the form $(a + b)^2$ and $(a - b)^2$.
• When expanding terms, always multiply the terms inside the parentheses.
• When combining terms, always add or subtract the coefficients of the terms.

Frequently Asked Questions

• Q: How do I simplify the expression $(2a - 3b)^2$? A: To simplify the expression $(2a - 3b)^2$, use the formula for expanding a squared binomial and expand the terms.
• Q: What is the final simplified form of the expression $(2a - 3b)^2$? A: The final simplified form of the expression $(2a - 3b)^2$ is $4a^2 - 12ab + 9b^2$.

Related Topics

• Simplifying expressions of the form $(a + b)^2$ and $(a - b)^2$
• Expanding terms using the distributive property
• Combining terms using the commutative and associative properties of addition and subtraction.
  

$$

Introduction

In our previous article, we discussed how to simplify the expression $(2a - 3b)^2$ using the formula for expanding a squared binomial. In this article, we will provide a Q&A section to help you better understand the concept and address any questions you may have.

Q&A

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

A: The formula for expanding a squared binomial is given by:

$$(a + b)^2 = a^2 + 2ab + b^2$$

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

Q: How do I simplify the expression $(2a - 3b)^2$?

A: To simplify the expression $(2a - 3b)^2$, use the formula for expanding a squared binomial and expand the terms. The steps are as follows:

1. Treat $2a$ as the first term and $-3b$ as the second term.
2. Use the formula for expanding a squared binomial.
3. Expand the terms using the distributive property.
4. Combine the terms using the commutative and associative properties of addition and subtraction.

Q: What is the final simplified form of the expression $(2a - 3b)^2$?

A: The final simplified form of the expression $(2a - 3b)^2$ is $4a^2 - 12ab + 9b^2$.

Q: Can I simplify the expression $(2a - 3b)^2$ further?

A: No, the expression $4a^2 - 12ab + 9b^2$ cannot be simplified further. It is the final simplified form of the original expression.

Q: What is the greatest common factor (GCF) of the terms in the expression $4a^2 - 12ab + 9b^2$?

A: The greatest common factor (GCF) of the terms in the expression $4a^2 - 12ab + 9b^2$ is 1.

Q: How do I expand the terms in the expression $(2a - 3b)^2$?

A: To expand the terms in the expression $(2a - 3b)^2$, use the distributive property. Multiply the first term $2a$ by the second term $-3b$ and then multiply the second term $-3b$ by the first term $2a$.

Q: Can I use the formula for expanding a squared binomial to simplify expressions of the form $(a + b)^2$ and $(a - b)^2$?

A: Yes, you can use the formula for expanding a squared binomial to simplify expressions of the form $(a + b)^2$ and $(a - b)^2$. The formula is given by:

$$(a + b)^2 = a^2 + 2ab + b^2$$

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

Additional Tips and Tricks

• When simplifying expressions, always look for the greatest common factor (GCF) of the terms.
• Use the formula for expanding a squared binomial to simplify expressions of the form $(a + b)^2$ and $(a - b)^2$.
• When expanding terms, always multiply the terms inside the parentheses.
• When combining terms, always add or subtract the coefficients of the terms.

Frequently Asked Questions

• Q: How do I simplify the expression $(2a - 3b)^2$? A: To simplify the expression $(2a - 3b)^2$, use the formula for expanding a squared binomial and expand the terms.
• Q: What is the final simplified form of the expression $(2a - 3b)^2$? A: The final simplified form of the expression $(2a - 3b)^2$ is $4a^2 - 12ab + 9b^2$.

Related Topics

• Simplifying expressions of the form $(a + b)^2$ and $(a - b)^2$
• Expanding terms using the distributive property
• Combining terms using the commutative and associative properties of addition and subtraction.