Expand And Combine Like Terms.$\left(3 - 8w^2\right)^2 = \square$

Feb 26, 2025 by ADMIN 66 views

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Introduction

In algebra, expanding and combining like terms is a crucial step in solving equations and simplifying expressions. It involves multiplying out the brackets and combining the like terms to get a simpler expression. In this article, we will explore how to expand and combine like terms using the example of the expression $\left(3 - 8w^2\right)^2$ .

What are Like Terms?

Like terms are terms that have the same variable(s) raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Expanding the Expression

To expand the expression $\left(3 - 8w^2\right)^2$ , we need to multiply out the brackets. This involves multiplying each term inside the brackets by each other term. We can use the distributive property to do this.

$\left(3 - 8w^2\right)^2 = (3 - 8w^2)(3 - 8w^2)$

Using the distributive property, we can multiply out the brackets as follows:

$(3 - 8w^2)(3 - 8w^2) = 3(3 - 8w^2) - 8w^2(3 - 8w^2)$

Expanding each term further, we get:

$3(3 - 8w^2) = 9 - 24w^2$

$-8w^2(3 - 8w^2) = -24w^2 + 64w^4$

Now, we can combine the two terms:

$9 - 24w^2 - 24w^2 + 64w^4$

Combining Like Terms

Now that we have expanded the expression, we can combine the like terms. We can see that the two terms $-24w^2$ are like terms, so we can combine them as follows:

$-24w^2 - 24w^2 = -48w^2$

Similarly, the two terms $9$ are like terms, but in this case, there is only one term, so we don't need to combine anything.

The final expression is:

$9 - 48w^2 + 64w^4$

Conclusion

In this article, we have seen how to expand and combine like terms using the example of the expression $\left(3 - 8w^2\right)^2$ . We have used the distributive property to multiply out the brackets and then combined the like terms to get a simpler expression. This is an important skill in algebra, and it can be used to solve equations and simplify expressions.

Examples

Here are a few more examples of expanding and combining like terms:

$\left(2x + 3\right)^2 = \left(2x + 3\right)\left(2x + 3\right) = 4x^2 + 12x + 9$
$\left(x - 2\right)^2 = \left(x - 2\right)\left(x - 2\right) = x^2 - 4x + 4$
$\left(3y - 2\right)^2 = \left(3y - 2\right)\left(3y - 2\right) = 9y^2 - 12y + 4$

Tips and Tricks

Here are a few tips and tricks to help you expand and combine like terms:

Make sure to use the distributive property to multiply out the brackets.
Identify the like terms and combine them.
Use the correct order of operations to simplify the expression.
Check your work by plugging in values for the variables.

Practice Problems

Here are a few practice problems to help you practice expanding and combining like terms:

$\left(x + 2\right)^2 = \left(x + 2\right)\left(x + 2\right) = ?$
$\left(3x - 2\right)^2 = \left(3x - 2\right)\left(3x - 2\right) = ?$
$\left(2x + 3\right)^2 = \left(2x + 3\right)\left(2x + 3\right) = ?$

Conclusion

In conclusion, expanding and combining like terms is an important skill in algebra. It involves multiplying out the brackets and combining the like terms to get a simpler expression. By following the steps outlined in this article, you can expand and combine like terms with ease. Remember to use the distributive property, identify the like terms, and use the correct order of operations to simplify the expression. With practice, you will become proficient in expanding and combining like terms.

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Introduction

In our previous article, we explored how to expand and combine like terms using the example of the expression $\left(3 - 8w^2\right)^2$ . We also provided some tips and tricks to help you practice expanding and combining like terms. In this article, we will answer some frequently asked questions about expanding and combining like terms.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I expand an expression with parentheses?

A: To expand an expression with parentheses, you need to multiply out the brackets using the distributive property. This involves multiplying each term inside the brackets by each other term.

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any numbers $a$ , $b$ , and $c$ , the following equation holds:

$a(b + c) = ab + ac$

This property can be used to multiply out brackets and expand expressions.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable(s) raised to the same power. Then, you can add or subtract the coefficients of these terms to get a simpler expression.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is as follows:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression with multiple terms?

A: To simplify an expression with multiple terms, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some common mistakes to avoid when expanding and combining like terms?

A: Some common mistakes to avoid when expanding and combining like terms include:

Forgetting to use the distributive property to multiply out brackets.
Failing to identify like terms and combine them.
Not following the order of operations when simplifying an expression.
Making errors when multiplying or dividing terms.

Tips and Tricks

Here are a few more tips and tricks to help you expand and combine like terms:

Make sure to use the distributive property to multiply out brackets.
Identify the like terms and combine them.
Use the correct order of operations to simplify the expression.
Check your work by plugging in values for the variables.
Practice, practice, practice! The more you practice expanding and combining like terms, the more comfortable you will become with the process.

Conclusion

In conclusion, expanding and combining like terms is an important skill in algebra. By following the steps outlined in this article, you can expand and combine like terms with ease. Remember to use the distributive property, identify the like terms, and use the correct order of operations to simplify the expression. With practice, you will become proficient in expanding and combining like terms.

Practice Problems

Here are a few practice problems to help you practice expanding and combining like terms:

$\left(x + 2\right)^2 = \left(x + 2\right)\left(x + 2\right) = ?$
$\left(3x - 2\right)^2 = \left(3x - 2\right)\left(3x - 2\right) = ?$
$\left(2x + 3\right)^2 = \left(2x + 3\right)\left(2x + 3\right) = ?$

Resources

Here are a few resources to help you learn more about expanding and combining like terms:

Khan Academy: Expanding and Combining Like Terms
Mathway: Expanding and Combining Like Terms
Algebra.com: Expanding and Combining Like Terms