Rewrite In Simplest Terms: $9(7m - 10) + 7(-5m - 8$\]Answer:$\square$

Understanding the Problem

In this article, we will focus on simplifying a given algebraic expression, $9(7m - 10) + 7(-5m - 8)$. This expression involves the use of parentheses, multiplication, and addition/subtraction. Our goal is to simplify this expression by applying the rules of algebra.

Step 1: Distribute the Numbers Outside the Parentheses

To simplify the expression, we need to start by distributing the numbers outside the parentheses to the terms inside. This means multiplying each term inside the parentheses by the number outside.

Distributing 9 to the Terms Inside the First Parentheses

We will start by distributing 9 to the terms inside the first parentheses: $7m - 10$. To do this, we multiply 9 by each term inside the parentheses:

$$9(7m - 10) = 9(7m) - 9(10)$$

Using the distributive property, we can rewrite this as:

$$63m - 90$$

Distributing 7 to the Terms Inside the Second Parentheses

Next, we will distribute 7 to the terms inside the second parentheses: $-5m - 8$. To do this, we multiply 7 by each term inside the parentheses:

$$7(-5m - 8) = 7(-5m) - 7(8)$$

Using the distributive property, we can rewrite this as:

$$-35m - 56$$

Combining Like Terms

Now that we have distributed the numbers outside the parentheses, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

Combining the Constant Terms

We can combine the constant terms, $-90$ and $-56$, by adding them together:

$$-90 + (-56) = -146$$

Combining the Variable Terms

We can combine the variable terms, $63m$ and $-35m$, by adding them together:

$$63m + (-35m) = 28m$$

Simplifying the Expression

Now that we have combined like terms, we can simplify the expression by adding the constant term and the variable term:

$$28m - 146$$

The Final Answer

Therefore, the simplified expression is:

$$28m - 146$$

This is the final answer to the given algebraic expression.

Conclusion

Q: What is the distributive property in algebra?

A: The distributive property is a rule in algebra that allows us to distribute a number outside the parentheses to the terms inside. This means that we can multiply each term inside the parentheses by the number outside.

Q: How do I distribute a number outside the parentheses?

A: To distribute a number outside the parentheses, you need to multiply each term inside the parentheses by the number outside. For example, if we have the expression $9(7m - 10)$, we would multiply 9 by each term inside the parentheses: $9(7m) - 9(10)$.

Q: What are like terms in algebra?

A: Like terms are terms that have the same variable 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 combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if we have the expression $3x + 2x$, we would combine the like terms by adding the coefficients: $3x + 2x = 5x$.

Q: What is the order of operations in algebra?

A: The order of operations in algebra is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

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

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

1. Distribute any numbers outside the parentheses to the terms inside.
2. Combine like terms.
3. Simplify any exponential expressions.
4. Evaluate any multiplication and division operations.
5. Finally, evaluate any addition and subtraction operations.

Q: What are some common algebraic expressions that I should know how to simplify?

A: Some common algebraic expressions that you should know how to simplify include:

• $a(b + c)$
• $a(b - c)$
• $a(b + c) + d$
• $a(b - c) + d$
• $a(b + c) - d$
• $a(b - c) - d$

Q: How do I know when to use the distributive property?

A: You should use the distributive property when you have an expression with parentheses and you need to multiply a number outside the parentheses to the terms inside.

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

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Forgetting to distribute a number outside the parentheses to the terms inside.
• Not combining like terms.
• Not following the order of operations.
• Making errors when multiplying or dividing.

Conclusion

In this article, we have answered some frequently asked questions about simplifying algebraic expressions. We have covered topics such as the distributive property, like terms, combining like terms, and the order of operations. By following these steps and avoiding common mistakes, you should be able to simplify algebraic expressions with ease.