Simplify The Expression. Write Your Answer In Standard Form.${ \left(\frac{2}{3} R+7\right)\left(\frac{2}{3} R-7\right) }$

Introduction

In this article, we will explore the process of simplifying a given algebraic expression. The expression we will be working with is a product of two binomials, each containing a variable and a constant. Our goal is to simplify this expression and write it in standard form.

The Expression

The given expression is:

$$\left(\frac{2}{3} r+7\right)\left(\frac{2}{3} r-7\right)$$

Step 1: Identify the Type of Expression

The given expression is a product of two binomials, which can be classified as a quadratic expression. A quadratic expression is a polynomial of degree two, which means it has a variable raised to the power of two.

Step 2: Apply the FOIL Method

To simplify the expression, we will use the FOIL method, which stands for "First, Outer, Inner, Last." This method involves multiplying the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Using the FOIL method, we get:

$$\left(\frac{2}{3} r+7\right)\left(\frac{2}{3} r-7\right)$$

$$=\left(\frac{2}{3} r\right)\left(\frac{2}{3} r\right)+\left(\frac{2}{3} r\right)\left(-7\right)+\left(7\right)\left(\frac{2}{3} r\right)+\left(7\right)\left(-7\right)$$

Step 3: Simplify the Expression

Now that we have applied the FOIL method, we can simplify the expression by combining like terms.

$$=\left(\frac{2}{3} r\right)\left(\frac{2}{3} r\right)+\left(\frac{2}{3} r\right)\left(-7\right)+\left(7\right)\left(\frac{2}{3} r\right)+\left(7\right)\left(-7\right)$$

$$=\frac{4}{9} r^2-\frac{14}{3} r+\frac{14}{3} r-49$$

Step 4: Combine Like Terms

Now that we have simplified the expression, we can combine like terms to get the final result.

$$=\frac{4}{9} r^2-\frac{14}{3} r+\frac{14}{3} r-49$$

$$=\frac{4}{9} r^2-49$$

Conclusion

In this article, we have simplified a given algebraic expression using the FOIL method and combining like terms. The final result is $\frac{4}{9} r^2-49$, which is the standard form of the expression.

Standard Form

The standard form of an algebraic expression is a way of writing the expression with the variable and constant terms separated and the variable terms in descending order of their exponents.

Example

Here is an example of how to write an algebraic expression in standard form:

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

This expression is already in standard form, with the variable term $2x^2$ first, followed by the linear term $3x$, and finally the constant term $-4$.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions:

• Use the FOIL method to multiply binomials.
• Combine like terms to simplify the expression.
• Write the expression in standard form to make it easier to read and understand.

Common Mistakes

Here are some common mistakes to avoid when simplifying algebraic expressions:

• Not using the FOIL method when multiplying binomials.
• Not combining like terms to simplify the expression.
• Not writing the expression in standard form.

Conclusion

Introduction

In our previous article, we explored the process of simplifying a given algebraic expression. We used the FOIL method and combined like terms to simplify the expression and write it in standard form. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is the FOIL method?

A: The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and involves multiplying the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I use the FOIL method?

A: To use the FOIL method, simply multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms. For example, if we have the expression $(x+3)(x+4)$, we would multiply the first terms to get $x \cdot x = x^2$, then the outer terms to get $x \cdot 4 = 4x$, then the inner terms to get $3 \cdot x = 3x$, and finally the last terms to get $3 \cdot 4 = 12$.

Q: What is the difference between the FOIL method and the distributive property?

A: The FOIL method and the distributive property are both used to multiply binomials, but they are used in different situations. The FOIL method is used when multiplying two binomials, while the distributive property is used when multiplying a binomial by a monomial.

Q: How do I combine like terms?

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

Q: What is the standard form of an algebraic expression?

A: The standard form of an algebraic expression is a way of writing the expression with the variable and constant terms separated and the variable terms in descending order of their exponents.

Q: How do I write an algebraic expression in standard form?

A: To write an algebraic expression in standard form, simply separate the variable and constant terms and arrange the variable terms in descending order of their exponents. For example, if we have the expression $3x^2 + 2x - 4$, we would write it in standard form as $3x^2 + 2x - 4$.

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

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

• Not using the FOIL method when multiplying binomials.
• Not combining like terms to simplify the expression.
• Not writing the expression in standard form.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through examples and exercises in a textbook or online resource. You can also try simplifying expressions on your own and checking your work with a calculator or online tool.

Conclusion

In conclusion, simplifying algebraic expressions is an important skill to have in mathematics. By using the FOIL method and combining like terms, you can simplify expressions and write them in standard form. Remember to use the tips and tricks provided in this article to help you simplify expressions, and avoid the common mistakes that can lead to errors.