Find The Product: { (t-7)(t+7) =$}$

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Introduction

In algebra, the product of two binomials is a fundamental concept that is used to simplify and solve equations. The product of two binomials can be found using the distributive property, which states that the product of two binomials is equal to the sum of the products of each term in the first binomial with each term in the second binomial. In this article, we will find the product of the two binomials $(t-7)$ and $(t+7)$.

Understanding the Problem

To find the product of the two binomials $(t-7)$ and $(t+7)$, we need to apply the distributive property. The distributive property states that for any three real numbers $a$, $b$, and $c$, the following equation holds:

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

We can use this property to find the product of the two binomials by multiplying each term in the first binomial with each term in the second binomial.

Applying the Distributive Property

To find the product of the two binomials $(t-7)$ and $(t+7)$, we can apply the distributive property as follows:

$(t-7)(t+7) = t(t+7) - 7(t+7)$

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression by multiplying each term in the first binomial with each term in the second binomial.

$t(t+7) = t^2 + 7t$

$-7(t+7) = -7t - 49$

Combining Like Terms

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

$t^2 + 7t - 7t - 49 = t^2 - 49$

Conclusion

In this article, we found the product of the two binomials $(t-7)$ and $(t+7)$ using the distributive property. We applied the distributive property to multiply each term in the first binomial with each term in the second binomial, and then simplified the expression by combining like terms. The final product is $t^2 - 49$.

Example Use Case

The product of two binomials can be used to solve equations and simplify expressions. For example, if we have the equation $(x+3)(x-2) = 0$, we can use the product of the two binomials to solve for $x$.

Tips and Tricks

• When multiplying two binomials, make sure to apply the distributive property correctly.
• When simplifying an expression, make sure to combine like terms.
• When solving an equation, make sure to use the product of the two binomials to simplify the expression.

Common Mistakes

• Failing to apply the distributive property correctly.
• Failing to combine like terms.
• Failing to use the product of the two binomials to simplify the expression.

Conclusion

In conclusion, finding the product of two binomials is a fundamental concept in algebra that can be used to simplify and solve equations. By applying the distributive property and combining like terms, we can find the product of two binomials. Remember to use the product of the two binomials to simplify the expression and solve for the variable.

Final Answer

The final answer is: $\boxed{t^2 - 49}$

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Introduction

In our previous article, we found the product of the two binomials $(t-7)$ and $(t+7)$ using the distributive property. In this article, we will answer some frequently asked questions about finding the product of two binomials.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that the product of two binomials is equal to the sum of the products of each term in the first binomial with each term in the second binomial.

Q: How do I apply the distributive property to find the product of two binomials?

A: To apply the distributive property, you need to multiply each term in the first binomial with each term in the second binomial. For example, to find the product of $(t-7)$ and $(t+7)$, you would multiply each term in the first binomial with each term in the second binomial.

Q: What is the difference between the product of two binomials and the sum of two binomials?

A: The product of two binomials is the result of multiplying each term in the first binomial with each term in the second binomial. The sum of two binomials is the result of adding each term in the first binomial with each term in the second binomial.

Q: How do I simplify an expression after finding the product of two binomials?

A: To simplify an expression after finding the product of two binomials, you need to combine like terms. Like terms are terms that have the same variable and exponent.

Q: What is the final product of $(t-7)$ and $(t+7)$?

A: The final product of $(t-7)$ and $(t+7)$ is $t^2 - 49$.

Q: Can I use the product of two binomials to solve equations?

A: Yes, you can use the product of two binomials to solve equations. For example, if you have the equation $(x+3)(x-2) = 0$, you can use the product of the two binomials to solve for $x$.

Q: What are some common mistakes to avoid when finding the product of two binomials?

A: Some common mistakes to avoid when finding the product of two binomials include failing to apply the distributive property correctly, failing to combine like terms, and failing to use the product of the two binomials to simplify the expression.

Example Use Case

The product of two binomials can be used to solve equations and simplify expressions. For example, if we have the equation $(x+3)(x-2) = 0$, we can use the product of the two binomials to solve for $x$.

Tips and Tricks

• When multiplying two binomials, make sure to apply the distributive property correctly.
• When simplifying an expression, make sure to combine like terms.
• When solving an equation, make sure to use the product of the two binomials to simplify the expression.

Common Mistakes

• Failing to apply the distributive property correctly.
• Failing to combine like terms.
• Failing to use the product of the two binomials to simplify the expression.

Conclusion

In conclusion, finding the product of two binomials is a fundamental concept in algebra that can be used to simplify and solve equations. By applying the distributive property and combining like terms, we can find the product of two binomials. Remember to use the product of the two binomials to simplify the expression and solve for the variable.

Final Answer

The final answer is: $\boxed{t^2 - 49}$