Rewrite The Expression In Standard Form: ${ Y = 2(x-3)(x+5) }$

Introduction

In algebra, it is often necessary to rewrite expressions in standard form, which is a way of writing an expression that is easy to read and understand. In this article, we will focus on rewriting the given expression in standard form. We will use the distributive property and other algebraic techniques to simplify the expression and rewrite it in standard form.

The Given Expression

The given expression is:

$$y = 2(x-3)(x+5)$$

This expression is a quadratic expression, which means it is a polynomial of degree two. The expression is already factored, which means it is written as a product of two binomials.

Rewriting the Expression in Standard Form

To rewrite the expression in standard form, we need to use the distributive property to expand the product of the two binomials. The distributive property states that for any real numbers a, b, and c:

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

We can use this property to expand the product of the two binomials in the given expression.

Step 1: Expand the Product

Using the distributive property, we can expand the product of the two binomials as follows:

$$y = 2(x-3)(x+5)$$

$$y = 2(x^2 + 5x - 3x - 15)$$

$$y = 2(x^2 + 2x - 15)$$

Step 2: Simplify the Expression

Now that we have expanded the product, we can simplify the expression by combining like terms. The expression can be simplified as follows:

$$y = 2x^2 + 4x - 30$$

The Final Answer

The final answer is:

$$y = 2x^2 + 4x - 30$$

This is the standard form of the given expression.

Conclusion

In this article, we have rewritten the given expression in standard form using the distributive property and other algebraic techniques. We have expanded the product of the two binomials and simplified the expression by combining like terms. The final answer is the standard form of the given expression.

Tips and Tricks

• When rewriting an expression in standard form, it is often helpful to use the distributive property to expand the product of the binomials.
• When simplifying an expression, it is often helpful to combine like terms.
• When working with quadratic expressions, it is often helpful to use the factored form to simplify the expression.

Common Mistakes

• When rewriting an expression in standard form, it is easy to make mistakes by not using the distributive property correctly.
• When simplifying an expression, it is easy to make mistakes by not combining like terms correctly.
• When working with quadratic expressions, it is easy to make mistakes by not using the factored form correctly.

Real-World Applications

• The standard form of a quadratic expression is often used in real-world applications such as physics, engineering, and economics.
• The standard form of a quadratic expression is often used to model real-world situations such as the motion of an object, the growth of a population, and the behavior of a system.

Further Reading

• For more information on rewriting expressions in standard form, see [1].
• For more information on the distributive property, see [2].
• For more information on quadratic expressions, see [3].

References: [1] Algebra, 2nd ed. by Michael Artin. [2] The Distributive Property, Math Open Reference. [3] Quadratic Expressions, Math Is Fun.

Glossary

• Distributive Property: A property of real numbers that states that for any real numbers a, b, and c, a(b+c) = ab + ac.
• Quadratic Expression: A polynomial of degree two, which means it is a polynomial with two terms.
• Standard Form: A way of writing an expression that is easy to read and understand.
• Binomial: A polynomial with two terms.
• Like Terms: Terms that have the same variable and exponent.
  Q&A: Rewriting Expressions in Standard Form =============================================

Introduction

In our previous article, we discussed how to rewrite expressions in standard form using the distributive property and other algebraic techniques. In this article, we will answer some common questions that students often have when it comes to rewriting expressions in standard form.

Q: What is the standard form of a quadratic expression?

A: The standard form of a quadratic expression is a way of writing the expression that is easy to read and understand. It is typically written in the form ax^2 + bx + c, where a, b, and c are real numbers.

Q: How do I rewrite a quadratic expression in standard form?

A: To rewrite a quadratic expression in standard form, you can use the distributive property to expand the product of the binomials. You can also use other algebraic techniques such as combining like terms to simplify the expression.

Q: What is the distributive property?

A: The distributive property is a property of real numbers that states that for any real numbers a, b, and c, a(b+c) = ab + ac. This property can be used to expand the product of two binomials.

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

A: To use the distributive property to rewrite a quadratic expression in standard form, you can follow these steps:

1. Expand the product of the two binomials using the distributive property.
2. Simplify the expression by combining like terms.
3. Write the expression in the standard form ax^2 + bx + c.

Q: What are some common mistakes to avoid when rewriting expressions in standard form?

A: Some common mistakes to avoid when rewriting expressions in standard form include:

• Not using the distributive property correctly.
• Not combining like terms correctly.
• Not writing the expression in the standard form ax^2 + bx + c.

Q: How do I check my work when rewriting an expression in standard form?

A: To check your work when rewriting an expression in standard form, you can follow these steps:

1. Rewrite the expression in standard form using the distributive property and other algebraic techniques.
2. Simplify the expression by combining like terms.
3. Check that the expression is in the standard form ax^2 + bx + c.

Q: What are some real-world applications of rewriting expressions in standard form?

A: Some real-world applications of rewriting expressions in standard form include:

• Modeling the motion of an object using quadratic expressions.
• Modeling the growth of a population using quadratic expressions.
• Modeling the behavior of a system using quadratic expressions.

Q: How do I practice rewriting expressions in standard form?

A: To practice rewriting expressions in standard form, you can try the following:

• Work through examples of quadratic expressions and rewrite them in standard form.
• Use online resources such as math websites and apps to practice rewriting expressions in standard form.
• Ask a teacher or tutor for help if you need it.

Conclusion

In this article, we have answered some common questions that students often have when it comes to rewriting expressions in standard form. We have discussed the standard form of a quadratic expression, how to rewrite a quadratic expression in standard form, and some common mistakes to avoid. We have also discussed some real-world applications of rewriting expressions in standard form and how to practice rewriting expressions in standard form.

Tips and Tricks

• When rewriting an expression in standard form, it is often helpful to use the distributive property to expand the product of the binomials.
• When simplifying an expression, it is often helpful to combine like terms.
• When working with quadratic expressions, it is often helpful to use the factored form to simplify the expression.

Common Mistakes

• When rewriting an expression in standard form, it is easy to make mistakes by not using the distributive property correctly.
• When simplifying an expression, it is easy to make mistakes by not combining like terms correctly.
• When working with quadratic expressions, it is easy to make mistakes by not using the factored form correctly.

Real-World Applications

• The standard form of a quadratic expression is often used in real-world applications such as physics, engineering, and economics.
• The standard form of a quadratic expression is often used to model real-world situations such as the motion of an object, the growth of a population, and the behavior of a system.

Further Reading

• For more information on rewriting expressions in standard form, see [1].
• For more information on the distributive property, see [2].
• For more information on quadratic expressions, see [3].

References: [1] Algebra, 2nd ed. by Michael Artin. [2] The Distributive Property, Math Open Reference. [3] Quadratic Expressions, Math Is Fun.

Glossary

• Distributive Property: A property of real numbers that states that for any real numbers a, b, and c, a(b+c) = ab + ac.
• Quadratic Expression: A polynomial of degree two, which means it is a polynomial with two terms.
• Standard Form: A way of writing an expression that is easy to read and understand.
• Binomial: A polynomial with two terms.
• Like Terms: Terms that have the same variable and exponent.