Solving Mathematical Expressions with x2
In this article, we will walk through a detailed explanation of solving a mathematical expression involving the substitution of x2. We'll break down the steps and provide a clear solution, while also explaining the underlying algebraic principles.
Preliminary Concepts: Algebra and Substitution
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It is a powerful tool for solving problems and is widely used in various fields. One of the key techniques in algebra is the substitution method, which involves replacing a variable with a specific value to simplify and solve the equation.
Given Expression and Substitution
The problem at hand is to find the value of the expression 8x √x^3 – x^2 when x2.
Step 1: Substituting the Value of x
We are given that x2. Let's substitute this value into the expression:
8x √x^3 - x^2 where x2
Step 2: Simplifying the Expression
Now, we will simplify the expression step by step:
8(2) √2^3 - 2^2
8(2) √8 - 4
16 √8 - 4
16 √(2*2*2) - 4
16 * 2 - 4
32 - 4
28
Therefore, the value of the expression when x2 is 28.
Understanding the Algebraic Operations
Let's delve deeper into the algebraic operations involved in this problem:
Multiplication and Exponentiation
In the expression, we first multiplied 8 by x, which became 8(2), resulting in 16 when we substitute x2.
Radical and Exponential Simplification
The term √x^3 was simplified to √8. This is because 2^3 equals 8, and taking the square root of 8 results in √(2*2*2), which is 2 times the square root of 2.
The term x^2 is simply 2 squared, which is 4.
Mathematical Expressions and the Substitution Method
The substitution method is crucial in solving complex mathematical problems. It allows us to isolate variables and simplify expressions, making them more manageable. In this example, we used the method to find the value of the expression by substituting x2 and simplifying the terms.
Conclusion
Understanding and applying the substitution method is a fundamental skill in algebra. This technique can be used to solve a wide range of mathematical expressions and equations. By breaking down the problem into smaller, more manageable parts, we can arrive at the correct solution systematically.