Subtract:${6w^9 - \left(11w^9 + 4\right)}$Your Answer Should Be In Simplest Terms.Enter The Correct Answer.

Mar 11, 2025 by ADMIN 109 views

$Subtract: $6w^9 - \left(11w^9 + 4\right)$$

Understanding the Problem

When dealing with algebraic expressions, it's essential to apply the correct order of operations to simplify the given expression. In this case, we're required to subtract the expression $\left(11w^9 + 4\right)$ from $6w^9$ . To do this, we'll first apply the distributive property to remove the parentheses and then combine like terms.

Applying the Distributive Property

The distributive property states that for any real numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . We can use this property to remove the parentheses in the given expression.

6w^9 - \left(11w^9 + 4\right)

Using the distributive property, we can rewrite the expression as:

6w^9 - 11w^9 - 4

Combining Like Terms

Now that we've removed the parentheses, we can combine like terms. In this case, we have two terms with the same variable, $w^9$ . We can combine these terms by adding or subtracting their coefficients.

6w^9 - 11w^9 - 4

Combining the like terms, we get:

-5w^9 - 4

Simplifying the Expression

The expression $-5w^9 - 4$ is already in its simplest form. We can't simplify it further because there are no like terms to combine.

Conclusion

To subtract the expression $\left(11w^9 + 4\right)$ from $6w^9$ , we applied the distributive property to remove the parentheses and then combined like terms. The resulting expression is $-5w^9 - 4$ , which is the simplest form of the given expression.

Final Answer

The final answer is: $\boxed{-5w^9 - 4}$

Example Use Case

This problem can be used as an example in a mathematics class to demonstrate the application of the distributive property and combining like terms. Students can work through the problem step-by-step to understand the process of simplifying algebraic expressions.

Tips and Tricks

When dealing with algebraic expressions, it's essential to apply the correct order of operations.
Use the distributive property to remove parentheses and combine like terms.
Simplify the expression by combining like terms and removing any unnecessary parentheses.

Common Mistakes

Failing to apply the distributive property when removing parentheses.
Not combining like terms correctly.
Not simplifying the expression to its simplest form.

Frequently Asked Questions

Q: What is the distributive property, and how is it used in this problem?

A: The distributive property is a mathematical concept that allows us to remove parentheses by multiplying each term inside the parentheses by the factor outside the parentheses. In this problem, we use the distributive property to remove the parentheses and simplify the expression.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, we add or subtract the coefficients of the terms with the same variable. In this problem, we combine the terms $6w^9$ and $-11w^9$ by adding their coefficients, resulting in $-5w^9$ .

Q: What is the final answer to the problem?

A: The final answer to the problem is $-5w^9 - 4$ .

Q: Can I simplify the expression further?

A: No, the expression $-5w^9 - 4$ is already in its simplest form. There are no like terms to combine, and we cannot simplify it further.

Q: What is the order of operations, and how is it used in this problem?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. In this problem, we follow the order of operations by first removing the parentheses using the distributive property and then combining like terms.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid include failing to apply the distributive property when removing parentheses, not combining like terms correctly, and not simplifying the expression to its simplest form.

Q: How can I apply the distributive property to remove parentheses in an algebraic expression?

A: To apply the distributive property, we multiply each term inside the parentheses by the factor outside the parentheses. In this problem, we multiply $6w^9$ by $-1$ to get $-6w^9$ , and we multiply $4$ by $-1$ to get $-4$ .

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms involves adding or subtracting the coefficients of terms with the same variable, while simplifying an expression involves removing any unnecessary parentheses and combining like terms.

Q: Can I use the distributive property to remove parentheses in any algebraic expression?

A: Yes, the distributive property can be used to remove parentheses in any algebraic expression. However, it's essential to follow the order of operations and combine like terms correctly to simplify the expression.

Q: How can I check my work when simplifying an algebraic expression?

A: To check your work, you can plug in a value for the variable and simplify the expression using the order of operations. If the result is correct, then your work is correct.