Factor The Expression Below. $x^2 - 64$A. $(x + 8)(x - 8$\] B. $(x - 8)(x - 8$\] C. $(x - 16)(x - 4$\] D. $(x + 16)(x - 4$\]

Introduction

Factoring is a fundamental concept in algebra that involves expressing an algebraic expression as a product of simpler expressions. In this article, we will focus on factoring the expression $x^2 - 64$. 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 $x^2 - 64$

To factor the expression $x^2 - 64$, we can use the difference of squares formula. We can rewrite the expression as:

$$x^2 - 64 = x^2 - 8^2$$

Now, we can apply the difference of squares formula by substituting $a = x$ and $b = 8$:

$$x^2 - 8^2 = (x + 8)(x - 8)$$

Therefore, the factored form of the expression $x^2 - 64$ is $(x + 8)(x - 8)$.

Checking the Answer

To check our answer, we can multiply the two factors together to see if we get the original expression:

$$(x + 8)(x - 8) = x^2 - 8x + 8x - 64 = x^2 - 64$$

As we can see, the product of the two factors is indeed the original expression, which confirms that our answer is correct.

Conclusion

In this article, we have factored the expression $x^2 - 64$ using the difference of squares formula. We have shown that the factored form of the expression is $(x + 8)(x - 8)$. We have also checked our answer by multiplying the two factors together to see if we get the original expression. This confirms that our answer is correct.

Common Mistakes to Avoid

When factoring expressions, it is easy to make mistakes. Here are some common mistakes to avoid:

• Not using the difference of squares formula: The difference of squares formula is a powerful tool in algebra, and it can be used to factor expressions of the form $x^2 - y^2$. Make sure to use this formula when factoring expressions of this form.
• Not checking the answer: It is easy to make mistakes when factoring expressions. Make sure to check your answer by multiplying the two factors together to see if you get the original expression.
• Not using the correct signs: When factoring expressions, make sure to use the correct signs. For example, when factoring the expression $x^2 - 64$, we used the signs $(x + 8)$ and $(x - 8)$.

Tips and Tricks

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

• Use the difference of squares formula: The difference of squares formula is a powerful tool in algebra, and it can be used to factor expressions of the form $x^2 - y^2$.
• Check your answer: Make sure to check your answer by multiplying the two factors together to see if you get the original expression.
• Use the correct signs: When factoring expressions, make sure to use the correct signs.

Practice Problems

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

• Factor the expression $x^2 - 25$: Use the difference of squares formula to factor the expression $x^2 - 25$.
• Factor the expression $x^2 - 9$: Use the difference of squares formula to factor the expression $x^2 - 9$.
• Factor the expression $x^2 - 36$: Use the difference of squares formula to factor the expression $x^2 - 36$.

Conclusion

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Introduction

In our previous article, we discussed how to factor the expression $x^2 - 64$ using the difference of squares formula. In this article, we will provide a Q&A guide to help you understand the concept of factoring expressions and how to apply it to different types of expressions.

Q: What is factoring?

A: Factoring is a process of expressing an algebraic expression as a product of simpler expressions. It involves breaking down an expression into its constituent parts and expressing it in a factored form.

Q: What is the difference of squares formula?

A: The difference of squares formula is a mathematical formula 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 $b$ that are being subtracted. Then, you can apply the formula by substituting $a$ and $b$ into the formula:

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

For example, to factor the expression $x^2 - 64$, you can identify $a = x$ and $b = 8$. Then, you can apply the formula by substituting $a$ and $b$ into the formula:

$$x^2 - 8^2 = (x + 8)(x - 8)$$

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

A: Here are some common mistakes to avoid when factoring expressions:

• Not using the difference of squares formula: The difference of squares formula is a powerful tool in algebra, and it can be used to factor expressions of the form $x^2 - y^2$. Make sure to use this formula when factoring expressions of this form.
• Not checking the answer: It is easy to make mistakes when factoring expressions. Make sure to check your answer by multiplying the two factors together to see if you get the original expression.
• Not using the correct signs: When factoring expressions, make sure to use the correct signs. For example, when factoring the expression $x^2 - 64$, we used the signs $(x + 8)$ and $(x - 8)$.

Q: How do I check my answer when factoring expressions?

A: To check your answer when factoring expressions, you need to multiply the two factors together to see if you get the original expression. For example, to check the answer to the expression $x^2 - 64$, you can multiply the two factors together:

$$(x + 8)(x - 8) = x^2 - 8x + 8x - 64 = x^2 - 64$$

As you can see, the product of the two factors is indeed the original expression, which confirms that our answer is correct.

Q: What are some tips and tricks to help me factor expressions?

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

• Use the difference of squares formula: The difference of squares formula is a powerful tool in algebra, and it can be used to factor expressions of the form $x^2 - y^2$.
• Check your answer: Make sure to check your answer by multiplying the two factors together to see if you get the original expression.
• Use the correct signs: When factoring expressions, make sure to use the correct signs.

Q: What are some practice problems to help me practice factoring expressions?

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

• Factor the expression $x^2 - 25$: Use the difference of squares formula to factor the expression $x^2 - 25$.
• Factor the expression $x^2 - 9$: Use the difference of squares formula to factor the expression $x^2 - 9$.
• Factor the expression $x^2 - 36$: Use the difference of squares formula to factor the expression $x^2 - 36$.

Conclusion

In this article, we have provided a Q&A guide to help you understand the concept of factoring expressions and how to apply it to different types of expressions. We have discussed the difference of squares formula, how to factor expressions using this formula, and some common mistakes to avoid. We have also provided some tips and tricks to help you factor expressions and some practice problems to help you practice factoring expressions.