Rewrite The Expression:${ 5xy(4xy - 3y) }$

Rewrite the Expression: 5xy(4xy - 3y)

In this article, we will focus on rewriting the given expression, which involves the multiplication of several variables and constants. The expression is $5xy(4xy - 3y)$, and our goal is to simplify it using the rules of algebra. We will use various techniques such as the distributive property and the commutative property to rewrite the expression in a more manageable form.

Before we start rewriting the expression, let's break it down and understand its components. The expression consists of three main parts:

• $5xy$: This is a product of three variables and a constant. The variables are $x$ and $y$, and the constant is $5$.
• $(4xy - 3y)$: This is a difference of two products. The first product is $4xy$, and the second product is $3y$.

To rewrite the expression, we will use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We will also use the commutative property, which states that for any real numbers $a$ and $b$, $ab = ba$.

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

$$5xy(4xy - 3y) = 5xy(4xy) - 5xy(3y)$$

Now, we can use the commutative property to rearrange the terms:

$$5xy(4xy) - 5xy(3y) = 20x^2y^2 - 15xy^2$$

The expression $20x^2y^2 - 15xy^2$ is already simplified, but we can further simplify it by factoring out the common term $5xy^2$:

$$20x^2y^2 - 15xy^2 = 5xy^2(4x - 3)$$

In this article, we rewrote the given expression $5xy(4xy - 3y)$ using the distributive property and the commutative property. We broke down the expression into its components and simplified it step by step. The final simplified expression is $5xy^2(4x - 3)$.

The final answer is $\boxed{5xy^2(4x - 3)}$.

Here is the step-by-step solution to the problem:

1. Break down the expression into its components: $5xy$ and $(4xy - 3y)$.
2. Use the distributive property to rewrite the expression: $5xy(4xy - 3y) = 5xy(4xy) - 5xy(3y)$.
3. Use the commutative property to rearrange the terms: $5xy(4xy) - 5xy(3y) = 20x^2y^2 - 15xy^2$.
4. Factor out the common term $5xy^2$: $20x^2y^2 - 15xy^2 = 5xy^2(4x - 3)$.

Here are some tips and tricks to help you solve similar problems:

• Use the distributive property to rewrite expressions involving multiplication.
• Use the commutative property to rearrange terms.
• Factor out common terms to simplify expressions.
• Break down complex expressions into their components and simplify them step by step.

Here are some common mistakes to avoid when solving similar problems:

• Failing to use the distributive property when rewriting expressions.
• Failing to use the commutative property when rearranging terms.
• Failing to factor out common terms.
• Not breaking down complex expressions into their components.

The techniques used in this article have real-world applications in various fields such as:

• Algebra: The distributive property and the commutative property are used extensively in algebra to simplify expressions and solve equations.
• Calculus: The techniques used in this article are used in calculus to find derivatives and integrals.
• Physics: The techniques used in this article are used in physics to describe the motion of objects and to solve problems involving forces and energies.

In our previous article, we rewrote the expression $5xy(4xy - 3y)$ using the distributive property and the commutative property. In this article, we will answer some frequently asked questions (FAQs) related to rewriting the expression.

Q: What is the distributive property?

A: The distributive property is a mathematical rule that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that we can distribute the multiplication over the addition.

Q: How do I apply the distributive property to rewrite the expression?

A: To apply the distributive property, we need to multiply each term inside the parentheses by the term outside the parentheses. In this case, we multiply $5xy$ by each term inside the parentheses, which are $4xy$ and $-3y$.

Q: What is the commutative property?

A: The commutative property is a mathematical rule that states that for any real numbers $a$ and $b$, $ab = ba$. This means that the order of the terms does not change the result.

Q: How do I apply the commutative property to rewrite the expression?

A: To apply the commutative property, we need to rearrange the terms in the expression. In this case, we can rearrange the terms to get $20x^2y^2 - 15xy^2$.

Q: Can I simplify the expression further?

A: Yes, we can simplify the expression further by factoring out the common term $5xy^2$. This gives us $5xy^2(4x - 3)$.

Q: What are some common mistakes to avoid when rewriting the expression?

A: Some common mistakes to avoid when rewriting the expression include:

• Failing to use the distributive property when rewriting expressions.
• Failing to use the commutative property when rearranging terms.
• Failing to factor out common terms.
• Not breaking down complex expressions into their components.

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

A: The distributive property is used when we have an expression with multiple terms inside the parentheses, and we need to multiply each term by the term outside the parentheses. The commutative property is used when we have an expression with multiple terms, and we need to rearrange the terms.

Q: Can I use the distributive property and the commutative property together?

A: Yes, we can use the distributive property and the commutative property together to rewrite the expression. In this case, we use the distributive property to rewrite the expression, and then we use the commutative property to rearrange the terms.

Q: What are some real-world applications of rewriting the expression?

A: The techniques used in this article have real-world applications in various fields such as:

• Algebra: The distributive property and the commutative property are used extensively in algebra to simplify expressions and solve equations.
• Calculus: The techniques used in this article are used in calculus to find derivatives and integrals.
• Physics: The techniques used in this article are used in physics to describe the motion of objects and to solve problems involving forces and energies.

In conclusion, rewriting the expression $5xy(4xy - 3y)$ using the distributive property and the commutative property is a straightforward process that involves breaking down the expression into its components and simplifying it step by step. We hope that this Q&A article has helped to clarify any doubts you may have had about rewriting the expression.