Write 8a 3 2 3 in simplest form – Embark on a mathematical adventure with us as we delve into the intricacies of simplifying “8a 3 2 3”. Join us as we uncover the secrets of this enigmatic expression, exploring its terms, coefficients, and the fascinating world of algebraic operations.
Prepare to be amazed as we unravel the mysteries of equivalent expressions and witness the power of simplification in real-world scenarios.
Overview of the Expression
The mathematical notation “8a 3 2 3” represents an algebraic expression consisting of multiple terms with coefficients.
The different terms in the expression are as follows:
- 8a
- 3
- 2
- 3
The coefficients of the terms are:
- 8 (coefficient of a)
- None (coefficient of 3)
- None (coefficient of 2)
- None (coefficient of 3)
Simplifying the Expression
Simplifying algebraic expressions involves combining like terms, which are terms with the same variable raised to the same power. In this case, we have “8a 3 2 3”.
Step 1: Identify Like Terms
The expression has two terms with the variable “a”: 8a and 2a. These are like terms because they have the same variable and exponent.
Step 2: Combine Like Terms
Combine the coefficients of the like terms: 8 + 2 =
10. The simplified expression becomes
a 3 3
Step 3: Simplify Further
We can also simplify the remaining terms: 3 + 3 =
6. The final simplified expression is
a 6
Factors and Expansion
To expand an expression, we need to multiply all the factors together.
Identifying the Factors
The factors of “8a 3 2 3” are:
- 8
- a
- 3
- 2
- 3
Expanding the Expression
Expanding the expression using these factors gives us:
8a
- 3
- 2
- 3 = 48a6
Comparison to Other Forms
The expression “8a 323” can be written in several equivalent forms. Equivalent expressions are those that have the same value, even though they may look different.
Simplified Form
The simplified form of “8a 323” is 512a 9. This is because 8 can be written as 2 3, and 3 2can be written as 9. Therefore, 8a 323= 2 3– a 323= 2 3– a 9= 512a 9.
Factored Form
The factored form of “8a 323” is 8a 3(a 2) 3. This is because a 32can be written as (a 2) 3. Therefore, 8a 323= 8a 3(a 2) 3.
Expanded Form
The expanded form of “8a 323” is 8a 3– a 2– a 3. This is because a 32can be written as a 3– a 2. Therefore, 8a 323= 8a 3– a 2– a 3.
Applications and Examples
Simplifying expressions like “8a 3 2 3” has practical applications in various fields.
Real-World Examples, Write 8a 3 2 3 in simplest form
- Physics:Simplifying expressions is crucial in physics calculations, such as determining the motion of objects or the forces acting on them.
- Engineering:Engineers simplify expressions to design structures, calculate stresses, and optimize systems.
- Mathematics:In higher-level mathematics, simplifying expressions is essential for solving complex equations, proving theorems, and exploring mathematical concepts.
Solving Equations
Simplifying expressions can simplify solving equations. For example, consider the equation:
2(3x + 4) = 22
Simplifying the left side:
2(3x + 4) = 6x + 8
The simplified equation is:
6x + 8 = 22
This simplified form is easier to solve for x.
Simplifying Complex Calculations
Simplifying expressions can make complex calculations more manageable. Consider the expression:
(x^2 + 2x)(x
3)
Expanding and simplifying:
(x^2 + 2x)(x
- 3) = x^3
- 3x^2 + 2x^2
- 6x = x^3
- x^2
- 6x
The simplified expression is more concise and easier to work with.
Helpful Answers: Write 8a 3 2 3 In Simplest Form
What is the simplified form of “8a 3 2 3”?
The simplified form is “10a 3”.
How do I combine like terms in “8a 3 2 3”?
Combine the coefficients of like terms. For example, combine “8a” and “2a” to get “10a”.
What are the factors of “8a 3 2 3”?
The factors are “2a” and “4a 3”.
