Factor The Expression $x^2 - 49$.A. $(x + 49)(x - 1)$ B. $ ( X + 7 ) ( X + 7 ) (x + 7)(x + 7) ( X + 7 ) ( X + 7 ) [/tex] C. $(x + 7)(x - 7)$ D. $(x - 7)(x - 7)$

Introduction

Factoring an expression is a fundamental concept in algebra that involves expressing a given expression as a product of simpler expressions. In this article, we will focus on factoring the expression $x^2 - 49$. This expression can be factored using the difference of squares formula, which is a powerful tool in algebra.

The Difference of Squares Formula

The difference of squares formula states that for any two expressions $a$ and $b$, the following equation holds:

$$a^2 - b^2 = (a + b)(a - b)$$

This formula can be used to factor expressions of the form $x^2 - y^2$, where $x$ and $y$ are any two expressions.

Factoring the Expression $x^2 - 49$

To factor the expression $x^2 - 49$, we can use the difference of squares formula. In this case, we have:

$$x^2 - 49 = x^2 - 7^2$$

Using the difference of squares formula, we can write:

$$x^2 - 7^2 = (x + 7)(x - 7)$$

Therefore, the factored form of the expression $x^2 - 49$ is $(x + 7)(x - 7)$.

Comparing the Factored Form with the Options

Now that we have factored the expression $x^2 - 49$, let's compare it with the options given:

• A. $(x + 49)(x - 1)$
• B. $(x + 7)(x + 7)$
• C. $(x + 7)(x - 7)$
• D. $(x - 7)(x - 7)$

From the factored form we obtained earlier, we can see that the correct answer is:

• C. $(x + 7)(x - 7)$

Conclusion

In this article, we have factored the expression $x^2 - 49$ using the difference of squares formula. We have also compared the factored form with the options given and identified the correct answer. Factoring expressions is an essential skill in algebra, and this article has provided a step-by-step guide on how to factor the expression $x^2 - 49$.

Tips and Tricks

Here are some tips and tricks to help you factor expressions:

• Use the difference of squares formula to factor expressions of the form $x^2 - y^2$.
• Look for common factors in the expression.
• Use the distributive property to expand the expression and identify the factors.
• Use the factored form to simplify the expression and solve equations.

Practice Problems

Here are some practice problems to help you practice factoring expressions:

• Factor the expression $x^2 - 16$.
• Factor the expression $x^2 - 9$.
• Factor the expression $x^2 - 25$.

Solutions

Here are the solutions to the practice problems:

• $x^2 - 16 = (x + 4)(x - 4)$
• $x^2 - 9 = (x + 3)(x - 3)$
• $x^2 - 25 = (x + 5)(x - 5)$

Conclusion

$$

Introduction

Factoring expressions is a fundamental concept in algebra that involves expressing a given expression as a product of simpler expressions. In our previous article, we provided a step-by-step guide on how to factor the expression $x^2 - 49$. In this article, we will answer some frequently asked questions about factoring expressions.

Q&A

Q: What is factoring an expression?

A: Factoring an expression involves expressing a given expression as a product of simpler expressions. This is done by identifying the common factors in the expression and rewriting it as a product of those factors.

Q: What is the difference of squares formula?

A: The difference of squares formula is a powerful tool in algebra that states that for any two expressions $a$ and $b$, the following equation holds:

$$a^2 - b^2 = (a + b)(a - b)$$

This formula can be used to factor expressions of the form $x^2 - y^2$, where $x$ and $y$ are any two expressions.

Q: How do I factor an expression using the difference of squares formula?

A: To factor an expression using the difference of squares formula, you need to identify the two expressions $a$ and $b$ in the expression. Then, you can use the formula to rewrite the expression as a product of two binomials.

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

A: Some common mistakes to avoid when factoring expressions include:

• Not identifying the common factors in the expression
• Not using the difference of squares formula when it is applicable
• Not checking the factored form to ensure that it is correct

Q: How do I check if a factored form is correct?

A: To check if a factored form is correct, you can multiply the two binomials together and see if you get the original expression. If you do, then the factored form is correct.

Q: What are some tips and tricks for factoring expressions?

A: Some tips and tricks for factoring expressions include:

• Using the difference of squares formula to factor expressions of the form $x^2 - y^2$
• Looking for common factors in the expression
• Using the distributive property to expand the expression and identify the factors
• Using the factored form to simplify the expression and solve equations

Q: How do I factor expressions with variables and constants?

A: To factor expressions with variables and constants, you need to identify the common factors in the expression and rewrite it as a product of those factors. You can use the difference of squares formula to factor expressions of the form $x^2 - y^2$, where $x$ and $y$ are any two expressions.

Q: What are some examples of factoring expressions?

A: Some examples of factoring expressions include:

• Factoring the expression $x^2 - 49$ using the difference of squares formula
• Factoring the expression $x^2 - 16$ using the difference of squares formula
• Factoring the expression $x^2 - 9$ using the difference of squares formula

Conclusion

Factoring expressions is an essential skill in algebra that involves expressing a given expression as a product of simpler expressions. In this article, we have answered some frequently asked questions about factoring expressions and provided some tips and tricks for factoring expressions. With practice and patience, you can master the art of factoring expressions and solve equations with ease.

Practice Problems

Here are some practice problems to help you practice factoring expressions:

• Factor the expression $x^2 - 25$.
• Factor the expression $x^2 - 36$.
• Factor the expression $x^2 - 49$.

Solutions

Here are the solutions to the practice problems:

• $x^2 - 25 = (x + 5)(x - 5)$
• $x^2 - 36 = (x + 6)(x - 6)$
• $x^2 - 49 = (x + 7)(x - 7)$

Conclusion

Factoring expressions is an essential skill in algebra that involves expressing a given expression as a product of simpler expressions. In this article, we have answered some frequently asked questions about factoring expressions and provided some tips and tricks for factoring expressions. With practice and patience, you can master the art of factoring expressions and solve equations with ease.