Simplify The Expression:$-7v^2 - 25v - 12$

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Introduction

In mathematics, simplifying expressions is a crucial step in solving equations and inequalities. It involves rewriting the expression in a more compact and manageable form, often by combining like terms. In this article, we will focus on simplifying the given expression: $-7v^2 - 25v - 12$. We will use various techniques to rewrite the expression in a simpler form.

Understanding the Expression

The given expression is a quadratic expression in the variable $v$. It consists of three terms: $-7v^2$, $-25v$, and $-12$. The first term is a squared term, while the second and third terms are linear terms.

Factoring the Expression

One way to simplify the expression is to factor it. Factoring involves expressing the expression as a product of two or more simpler expressions. In this case, we can try to factor the expression by grouping the terms.

-7v^2 - 25v - 12
= -7v^2 - 28v + 3v - 12
= -7v(v + 4) + 3(v + 4)

Using the Distributive Property

We can use the distributive property to simplify the expression further. The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

-7v(v + 4) + 3(v + 4)
= -7v^2 - 28v + 3v + 12
= -7v^2 - 25v + 12

Combining Like Terms

We can combine like terms to simplify the expression further. Like terms are terms that have the same variable raised to the same power.

-7v^2 - 25v + 12
= -7v^2 - 25v - 12 + 12 + 12
= -7v^2 - 25v - 12 + 24
= -7v^2 - 25v + 12

Final Simplification

After combining like terms, we can simplify the expression further by factoring out the greatest common factor (GCF). The GCF is the largest expression that divides each term in the expression.

-7v^2 - 25v + 12
= -7v^2 - 28v + 3v + 12
= -7v(v + 4) + 3(v + 4)
= (-7v + 3)(v + 4)

Conclusion

In this article, we simplified the expression $-7v^2 - 25v - 12$ using various techniques. We factored the expression, used the distributive property, combined like terms, and finally simplified the expression by factoring out the GCF. The final simplified expression is $(-7v + 3)(v + 4)$.

Frequently Asked Questions

• Q: What is the greatest common factor (GCF) of the expression $-7v^2 - 25v - 12$? A: The GCF of the expression is 1.
• Q: How do I simplify a quadratic expression? A: To simplify a quadratic expression, you can factor it, use the distributive property, combine like terms, and finally simplify the expression by factoring out the GCF.
• Q: What is the final simplified expression of $-7v^2 - 25v - 12$? A: The final simplified expression is $(-7v + 3)(v + 4)$.

Further Reading

• Quadratic Expressions: A quadratic expression is a polynomial expression of degree two. It can be written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.
• Factoring Quadratic Expressions: Factoring a quadratic expression involves expressing it as a product of two or more simpler expressions.
• Distributive Property: The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

References

• [1] "Quadratic Expressions" by Math Open Reference. Retrieved February 2023.
• [2] "Factoring Quadratic Expressions" by Mathway. Retrieved February 2023.
• [3] "Distributive Property" by Khan Academy. Retrieved February 2023.
  

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Introduction

In our previous article, we simplified the expression $-7v^2 - 25v - 12$ using various techniques. We factored the expression, used the distributive property, combined like terms, and finally simplified the expression by factoring out the greatest common factor (GCF). In this article, we will answer some frequently asked questions related to simplifying quadratic expressions.

Q&A

Q: What is the greatest common factor (GCF) of the expression $-7v^2 - 25v - 12$?

A: The GCF of the expression is 1.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you can factor it, use the distributive property, combine like terms, and finally simplify the expression by factoring out the GCF.

Q: What is the final simplified expression of $-7v^2 - 25v - 12$?

A: The final simplified expression is $(-7v + 3)(v + 4)$.

Q: Can I simplify a quadratic expression by adding or subtracting the terms?

A: No, you cannot simplify a quadratic expression by adding or subtracting the terms. Simplifying a quadratic expression involves factoring, using the distributive property, combining like terms, and finally simplifying the expression by factoring out the GCF.

Q: How do I factor a quadratic expression?

A: To factor a quadratic expression, you can look for two binomials whose product is the original expression. You can also use the distributive property to factor the expression.

Q: What is the distributive property?

A: The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Q: Can I simplify a quadratic expression by using the distributive property?

A: Yes, you can simplify a quadratic expression by using the distributive property. The distributive property can be used to factor the expression and simplify it.

Q: How do I combine like terms in a quadratic expression?

A: To combine like terms in a quadratic expression, you can add or subtract the coefficients of the like terms.

Q: What are like terms in a quadratic expression?

A: Like terms in a quadratic expression are terms that have the same variable raised to the same power.

Q: Can I simplify a quadratic expression by using the greatest common factor (GCF)?

A: Yes, you can simplify a quadratic expression by using the greatest common factor (GCF). The GCF can be used to factor out the common factor from the expression.

Q: How do I find the greatest common factor (GCF) of a quadratic expression?

A: To find the greatest common factor (GCF) of a quadratic expression, you can look for the largest expression that divides each term in the expression.

Conclusion

In this article, we answered some frequently asked questions related to simplifying quadratic expressions. We discussed the greatest common factor (GCF), factoring, using the distributive property, combining like terms, and finally simplifying the expression by factoring out the GCF. We hope that this article has been helpful in understanding how to simplify quadratic expressions.

Frequently Asked Questions

• Q: What is the greatest common factor (GCF) of the expression $-7v^2 - 25v - 12$? A: The GCF of the expression is 1.
• Q: How do I simplify a quadratic expression? A: To simplify a quadratic expression, you can factor it, use the distributive property, combine like terms, and finally simplify the expression by factoring out the GCF.
• Q: What is the final simplified expression of $-7v^2 - 25v - 12$? A: The final simplified expression is $(-7v + 3)(v + 4)$.

Further Reading

• Quadratic Expressions: A quadratic expression is a polynomial expression of degree two. It can be written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.
• Factoring Quadratic Expressions: Factoring a quadratic expression involves expressing it as a product of two or more simpler expressions.
• Distributive Property: The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

References

• [1] "Quadratic Expressions" by Math Open Reference. Retrieved February 2023.
• [2] "Factoring Quadratic Expressions" by Mathway. Retrieved February 2023.
• [3] "Distributive Property" by Khan Academy. Retrieved February 2023.