Simplify The Expression: \[$(4n - 1)(-n + 3)\$\]
Simplify the Expression: (4n - 1)(-n + 3)
In algebra, simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical statements. In this article, we will focus on simplifying the given expression: {(4n - 1)(-n + 3)$}$. We will use the distributive property and other algebraic techniques to simplify the expression.
Understanding the Distributive Property
The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression. The distributive property can be written as:
a(b + c) = ab + ac
This property can be applied to both addition and subtraction. For example:
a(b - c) = ab - ac
Simplifying the Expression
To simplify the given expression, we will use the distributive property to expand the product of the two binomials:
{(4n - 1)(-n + 3)$}$
Using the distributive property, we can write:
{(4n - 1)(-n + 3) = (4n)(-n) + (4n)(3) - (1)(-n) - (1)(3)$}$
Now, we can simplify each term:
{(4n)(-n) = -4n^2$}$
{(4n)(3) = 12n$}$
{-(1)(-n) = n$}$
{-(1)(3) = -3$}$
So, the simplified expression is:
{-4n^2 + 12n + n - 3$}$
Combining like terms, we get:
{-4n^2 + 13n - 3$}$
In this article, we simplified the given expression using the distributive property and other algebraic techniques. We expanded the product of the two binomials and simplified each term. The final simplified expression is:
{-4n^2 + 13n - 3$}$
This expression can be used to solve equations and manipulate mathematical statements.
- When simplifying expressions, always use the distributive property to expand the product of binomials.
- Combine like terms to simplify the expression.
- Use algebraic techniques such as factoring and canceling to further simplify the expression.
- Simplify the expression: {(2x + 1)(x - 2)$}$
- Simplify the expression: {(3y - 2)(y + 1)$}$
- Binomial: An expression consisting of two terms, such as 2x + 3 or x - 2.
- Distributive Property: A fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression.
- Simplify: To reduce an expression to its simplest form by combining like terms and using algebraic techniques.
Simplify the Expression: (4n - 1)(-n + 3) - Q&A
In our previous article, we simplified the expression: {(4n - 1)(-n + 3)$}$. We used the distributive property and other algebraic techniques to simplify the expression. In this article, we will answer some frequently asked questions related to simplifying expressions.
Q: What is the distributive property?
A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression. It can be written as:
a(b + c) = ab + ac
Q: How do I simplify an expression using the distributive property?
A: To simplify an expression using the distributive property, you need to multiply each term in one expression by each term in another expression. For example, to simplify the expression: {(4n - 1)(-n + 3)$}$, you would multiply each term in the first expression by each term in the second expression:
{(4n - 1)(-n + 3) = (4n)(-n) + (4n)(3) - (1)(-n) - (1)(3)$}$
Q: What is the difference between simplifying and factoring?
A: Simplifying and factoring are two different algebraic techniques. Simplifying involves reducing an expression to its simplest form by combining like terms and using algebraic techniques. Factoring involves expressing an expression as a product of simpler expressions.
Q: How do I know when to simplify or factor an expression?
A: You should simplify an expression when it is in the form of a product of two or more expressions, and you want to reduce it to its simplest form. You should factor an expression when it is in the form of a polynomial, and you want to express it as a product of simpler expressions.
Q: Can I simplify an expression with variables and constants?
A: Yes, you can simplify an expression with variables and constants. For example, to simplify the expression: {(4x + 2)(x - 3)$}$, you would multiply each term in the first expression by each term in the second expression:
{(4x + 2)(x - 3) = (4x)(x) + (4x)(-3) + (2)(x) + (2)(-3)$}$
Q: How do I know when to use the distributive property?
A: You should use the distributive property when you need to expand an expression by multiplying each term in one expression by each term in another expression.
Q: Can I simplify an expression with fractions?
A: Yes, you can simplify an expression with fractions. For example, to simplify the expression: {(2x + 1)(x - 2)$}$, you would multiply each term in the first expression by each term in the second expression:
{(2x + 1)(x - 2) = (2x)(x) + (2x)(-2) + (1)(x) + (1)(-2)$}$
In this article, we answered some frequently asked questions related to simplifying expressions. We discussed the distributive property, simplifying and factoring, and how to simplify expressions with variables and constants. We also provided examples of how to simplify expressions with fractions.
- Always use the distributive property to expand expressions by multiplying each term in one expression by each term in another expression.
- Combine like terms to simplify the expression.
- Use algebraic techniques such as factoring and canceling to further simplify the expression.
- Simplify the expression: {(2x + 1)(x - 2)$}$
- Simplify the expression: {(3y - 2)(y + 1)$}$
- Binomial: An expression consisting of two terms, such as 2x + 3 or x - 2.
- Distributive Property: A fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression.
- Simplify: To reduce an expression to its simplest form by combining like terms and using algebraic techniques.