Use The Distributive Property To Rewrite The Expression. Write Your Answer In Standard Form.\[$(x+5)(x-4) =\$\] \[$\square\$\]

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside the parentheses. In this article, we will use the distributive property to rewrite the given expression in standard form.

The Given Expression

The given expression is $(x+5)(x-4)$. Our goal is to rewrite this expression using the distributive property.

Applying the Distributive Property

To apply the distributive property, we need to multiply each term inside the parentheses with the term outside the parentheses. In this case, we have two sets of parentheses, so we will multiply each term in the first parentheses with each term in the second parentheses.

Step 1: Multiply the First Term in the First Parentheses with Each Term in the Second Parentheses

The first term in the first parentheses is $x$. We will multiply this term with each term in the second parentheses, which are $x$ and $-4$.

$x \cdot x = x^2$ $x \cdot -4 = -4x$

Step 2: Multiply the Second Term in the First Parentheses with Each Term in the Second Parentheses

The second term in the first parentheses is $5$. We will multiply this term with each term in the second parentheses, which are $x$ and $-4$.

$5 \cdot x = 5x$ $5 \cdot -4 = -20$

Combining the Terms

Now that we have multiplied each term in the first parentheses with each term in the second parentheses, we can combine the terms to get the final expression.

$x^2 - 4x + 5x - 20$

Simplifying the Expression

We can simplify the expression by combining like terms. In this case, we have two terms with the variable $x$, which are $-4x$ and $5x$. We can combine these terms by adding their coefficients.

$-4x + 5x = x$

So, the simplified expression is $x^2 + x - 20$.

Conclusion

In this article, we used the distributive property to rewrite the given expression $(x+5)(x-4)$ in standard form. We applied the distributive property by multiplying each term inside the parentheses with the term outside the parentheses, and then combined the terms to get the final expression. The final expression is $x^2 + x - 20$.

Example Problems

Here are a few example problems that demonstrate the use of the distributive property:

Example 1

$(x+3)(x-2) = ?$

Using the distributive property, we get:

$x \cdot x = x^2$ $x \cdot -2 = -2x$ $3 \cdot x = 3x$ $3 \cdot -2 = -6$

Combining the terms, we get:

$x^2 - 2x + 3x - 6$ $x^2 + x - 6$

Example 2

$(x-2)(x+4) = ?$

Using the distributive property, we get:

$x \cdot x = x^2$ $x \cdot 4 = 4x$ $-2 \cdot x = -2x$ $-2 \cdot 4 = -8$

Combining the terms, we get:

$x^2 + 4x - 2x - 8$ $x^2 + 2x - 8$

Example 3

$(x+1)(x-3) = ?$

Using the distributive property, we get:

$x \cdot x = x^2$ $x \cdot -3 = -3x$ $1 \cdot x = x$ $1 \cdot -3 = -3$

Combining the terms, we get:

$x^2 - 3x + x - 3$ $x^2 - 2x - 3$

Practice Problems

Here are a few practice problems that you can try to apply the distributive property:

Problem 1

$(x+2)(x-5) = ?$

Problem 2

$(x-3)(x+2) = ?$

Problem 3

$(x+4)(x-1) = ?$

Answer Key

Here are the answers to the practice problems:

Problem 1

$x^2 - 5x + 2x - 10$ $x^2 - 3x - 10$

Problem 2

$x^2 + 2x - 3x - 6$ $x^2 - x - 6$

Problem 3

$x^2 - x + 4x - 4$ $x^2 + 3x - 4$

Conclusion

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Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. This means that you will multiply each term in the first parentheses with each term in the second parentheses.

Q: What are the steps to apply the distributive property?

A: The steps to apply the distributive property are:

1. Multiply the first term in the first parentheses with each term in the second parentheses.
2. Multiply the second term in the first parentheses with each term in the second parentheses.
3. Combine the terms to get the final expression.

Q: How do I simplify the expression after applying the distributive property?

A: To simplify the expression, you need to combine like terms. This means that you need to add or subtract the coefficients of the terms with the same variable.

Q: What are some common mistakes to avoid when applying the distributive property?

A: Some common mistakes to avoid when applying the distributive property include:

• Not multiplying each term inside the parentheses with the term outside the parentheses.
• Not combining like terms after applying the distributive property.
• Not following the order of operations (PEMDAS).

Q: How do I use the distributive property to rewrite an expression in standard form?

A: To use the distributive property to rewrite an expression in standard form, you need to follow these steps:

1. Apply the distributive property by multiplying each term inside the parentheses with the term outside the parentheses.
2. Combine the terms to get the final expression.
3. Simplify the expression by combining like terms.

Q: What are some examples of expressions that can be rewritten using the distributive property?

A: Some examples of expressions that can be rewritten using the distributive property include:

• $(x+3)(x-2)$
• $(x-2)(x+4)$
• $(x+1)(x-3)$

Q: How do I check my work when applying the distributive property?

A: To check your work when applying the distributive property, you need to:

• Multiply each term inside the parentheses with the term outside the parentheses.
• Combine the terms to get the final expression.
• Simplify the expression by combining like terms.
• Check that the final expression is in standard form.

Q: What are some real-world applications of the distributive property?

A: Some real-world applications of the distributive property include:

• Algebraic expressions in physics and engineering.
• Financial calculations, such as calculating interest rates.
• Data analysis, such as calculating means and medians.

Q: How do I practice using the distributive property?

A: To practice using the distributive property, you can try the following:

• Work through example problems and practice exercises.
• Use online resources, such as calculators and worksheets.
• Ask a teacher or tutor for help and guidance.
• Practice applying the distributive property to different types of expressions.

Conclusion

In this article, we have answered some frequently asked questions about the distributive property. We have covered topics such as how to apply the distributive property, how to simplify expressions, and how to check your work. We have also provided examples of expressions that can be rewritten using the distributive property and some real-world applications of the distributive property.