Simplify The Expression: { (9v + 2)(10v - 5)$}$A. ${ 90v^2 + 65v + 10\$} B. ${ 90v^2 - 10\$} C. ${ 70v^2 - 19v - 12\$} D. ${ 90v^2 - 25v - 10\$}
Introduction
In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on simplifying a specific expression involving two binomials. We will use the distributive property to expand the expression and then combine like terms to simplify it.
The Expression to Simplify
The expression we need to simplify is:
{(9v + 2)(10v - 5)$}$
This expression involves two binomials, and we need to multiply them together to simplify it.
Step 1: Multiply the Binomials
To multiply the binomials, we will use the distributive property. This property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
We will apply this property to each term in the first binomial and multiply it by each term in the second binomial.
Multiplying the First Term
The first term in the first binomial is 9v. We will multiply this term by each term in the second binomial:
9v(10v) = 90v^2
9v(-5) = -45v
Multiplying the Second Term
The second term in the first binomial is 2. We will multiply this term by each term in the second binomial:
2(10v) = 20v
2(-5) = -10
Combining the Terms
Now that we have multiplied each term in the first binomial by each term in the second binomial, we can combine the terms:
90v^2 - 45v + 20v - 10
We can combine the like terms -45v and 20v to get:
-25v
So, the expression becomes:
90v^2 - 25v - 10
Conclusion
In this article, we simplified the expression {(9v + 2)(10v - 5)$}$ using the distributive property. We multiplied each term in the first binomial by each term in the second binomial and then combined the like terms to simplify the expression. The final simplified expression is:
${90v^2 - 25v - 10\$}
This expression matches option D in the given choices.
Key Takeaways
- To simplify an expression involving two binomials, we can use the distributive property to multiply each term in the first binomial by each term in the second binomial.
- We can then combine the like terms to simplify the expression.
- The final simplified expression is ${90v^2 - 25v - 10\$}.
Practice Problems
- Simplify the expression {(4x + 3)(2x - 1)$}$.
- Simplify the expression {(2y - 4)(3y + 2)$}$.
- Simplify the expression {(5z + 2)(z - 3)$}$.
Answer Key
- ${8x^2 + 5x - 3\$}
- ${6y^2 - 2y - 8\$}
- ${5z^2 - 13z - 6\$}
Additional Resources
For more practice problems and additional resources, visit the following websites:
- Khan Academy: Algebra
- Mathway: Algebra
- IXL: Algebra
Introduction
In our previous article, we simplified the expression {(9v + 2)(10v - 5)$}$ using the distributive property. We multiplied each term in the first binomial by each term in the second binomial and then combined the like terms to simplify the expression. In this article, we will answer some frequently asked questions about simplifying expressions involving two binomials.
Q&A
Q: What is the distributive property?
A: The distributive property is a mathematical concept that states that for any real numbers a, b, and c:
a(b + c) = ab + ac
This property allows us to multiply each term in one binomial by each term in another binomial.
Q: How do I apply the distributive property to simplify an expression?
A: To apply the distributive property, you need to multiply each term in the first binomial by each term in the second binomial. Then, combine the like terms to simplify the expression.
Q: What are like terms?
A: Like terms are terms that have the same variable(s) raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have 2x + 4x, you can combine the like terms by adding the coefficients: 2x + 4x = 6x.
Q: What if I have a negative coefficient?
A: If you have a negative coefficient, you need to change the sign of the coefficient when you combine like terms. For example, if you have -2x + 4x, you can combine the like terms by adding the coefficients: -2x + 4x = 2x.
Q: Can I simplify an expression with more than two binomials?
A: Yes, you can simplify an expression with more than two binomials by applying the distributive property multiple times. However, it's often easier to simplify the expression by multiplying the binomials in pairs.
Q: What if I get a negative sign in front of the expression?
A: If you get a negative sign in front of the expression, you can simply add a negative sign to the front of the expression. For example, if you have -(9v + 2)(10v - 5), you can simplify the expression by multiplying the binomials and then adding a negative sign to the front of the expression.
Conclusion
In this article, we answered some frequently asked questions about simplifying expressions involving two binomials. We covered topics such as the distributive property, like terms, and combining like terms. By following the steps outlined in this article, you can simplify expressions involving two binomials and become more confident in your algebra skills.
Practice Problems
- Simplify the expression {(3x + 2)(2x - 1)$}$.
- Simplify the expression {(4y - 3)(3y + 2)$}$.
- Simplify the expression {(5z + 1)(z - 2)$}$.
Answer Key
- ${6x^2 + x - 2\$}
- ${12y^2 - y - 6\$}
- ${5z^2 - 13z - 2\$}
Additional Resources
For more practice problems and additional resources, visit the following websites:
- Khan Academy: Algebra
- Mathway: Algebra
- IXL: Algebra
By following the steps outlined in this article, you can simplify expressions involving two binomials and become more confident in your algebra skills.