Simplify The Expression:$(4n + 3)(3n - 3$\]
Simplify the Expression: (4n + 3)(3n - 3)
In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the most common methods of simplifying expressions is by using the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this article, we will use the distributive property to simplify the expression (4n + 3)(3n - 3).
Understanding the Distributive Property
The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. For example, consider the expression (a + b)(c + d). Using the distributive property, we can expand this expression as follows:
(a + b)(c + d) = ac + ad + bc + bd
This means that we multiply each term inside the parentheses (a and b) with each term outside the parentheses (c and d).
Simplifying the Expression
Now that we have a good understanding of the distributive property, let's apply it to the expression (4n + 3)(3n - 3). We will multiply each term inside the parentheses (4n and 3) with each term outside the parentheses (3n and -3).
(4n + 3)(3n - 3) = (4n)(3n) + (4n)(-3) + (3)(3n) + (3)(-3)
Expanding the Terms
Now, let's expand each term in the expression.
(4n)(3n) = 12n^2
(4n)(-3) = -12n
(3)(3n) = 9n
(3)(-3) = -9
Combining Like Terms
Now that we have expanded each term, let's combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: -12n and 9n. We can combine these terms by adding their coefficients.
-12n + 9n = -3n
So, the simplified expression is:
12n^2 - 3n - 9
In this article, we used the distributive property to simplify the expression (4n + 3)(3n - 3). We expanded each term in the expression and then combined like terms to get the final simplified expression. This is a common technique used in algebra to simplify complex expressions and solve equations.
- When using the distributive property, make sure to multiply each term inside the parentheses with each term outside the parentheses.
- When expanding terms, make sure to follow the order of operations (PEMDAS).
- When combining like terms, make sure to add or subtract the coefficients of the like terms.
- Simplify the expression (2x + 5)(x - 2)
- Simplify the expression (3y - 2)(y + 4)
- Simplify the expression (x + 2)(x - 3)
- (2x + 5)(x - 2) = 2x^2 - 4x + 5x - 10 = 2x^2 + x - 10
- (3y - 2)(y + 4) = 3y^2 + 12y - 2y - 8 = 3y^2 + 10y - 8
- (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6
Simplify the Expression: (4n + 3)(3n - 3) - Q&A =====================================================
In our previous article, we used the distributive property to simplify the expression (4n + 3)(3n - 3). We expanded each term in the expression and then combined like terms to get the final simplified expression. In this article, we will answer some common 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 inside the parentheses with the term outside the parentheses.
Q: How do I apply the distributive property?
A: To apply the distributive property, you need to multiply each term inside the parentheses with each term outside the parentheses. For example, consider the expression (a + b)(c + d). Using the distributive property, we can expand this expression as follows:
(a + b)(c + d) = ac + ad + bc + bd
Q: What are like terms?
A: Like terms are terms that have the same variable 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, consider the expression 2x + 4x. We can combine these terms by adding their coefficients:
2x + 4x = 6x
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify complex expressions?
A: To simplify complex expressions, you need to use the distributive property to expand the expression, and then combine like terms. For example, consider the expression (2x + 3)(x - 2). We can simplify this expression as follows:
(2x + 3)(x - 2) = 2x^2 - 4x + 3x - 6
Combine like terms:
2x^2 - x - 6
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Not using the distributive property to expand expressions.
- Not combining like terms.
- Not following the order of operations.
- Not simplifying expressions completely.
In this article, we answered some common questions related to simplifying expressions. We discussed the distributive property, like terms, and the order of operations. We also provided some tips and tricks for simplifying complex expressions. By following these tips and tricks, you can simplify expressions like a pro!
- Make sure to use the distributive property to expand expressions.
- Make sure to combine like terms.
- Make sure to follow the order of operations.
- Make sure to simplify expressions completely.
- Simplify the expression (2x + 5)(x - 2)
- Simplify the expression (3y - 2)(y + 4)
- Simplify the expression (x + 2)(x - 3)
- (2x + 5)(x - 2) = 2x^2 - 4x + 5x - 10 = 2x^2 + x - 10
- (3y - 2)(y + 4) = 3y^2 + 12y - 2y - 8 = 3y^2 + 10y - 8
- (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6