-(x%5E3%2B7x%5E2-3x%2B1).jpeg "(-3x^3+5x^2+10x+4)-(x^3+7x^2-3x+1)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
Introduction
Algebraic expressions are a crucial part of mathematics, and simplifying them is an essential skill to master. In this article, we will explore the process of simplifying the algebraic expression (-3x^3+5x^2+10x+4)-(x^3+7x^2-3x+1). We will break down the steps to combine like terms and arrive at a simplified expression.
The Given Expression
The given expression is:
(-3x^3+5x^2+10x+4)-(x^3+7x^2-3x+1)
Our goal is to simplify this expression by combining like terms.
Step 1: Distribute the Negative Sign
To begin, we need to distribute the negative sign to the entire expression inside the parentheses:
-3x^3 + 5x^2 + 10x + 4 - x^3 - 7x^2 + 3x - 1
Step 2: Combine Like Terms
Next, we combine like terms, which are terms with the same variable (x) and exponent. We start by combining the x^3 terms:
-4x^3 + ...
Then, we combine the x^2 terms:
-4x^3 - 2x^2 + ...
Now, we combine the x terms:
-4x^3 - 2x^2 + 13x + ...
Finally, we combine the constant terms:
-4x^3 - 2x^2 + 13x + 3
Simplified Expression
The simplified expression is:
-4x^3 - 2x^2 + 13x + 3
Conclusion
In this article, we have demonstrated the step-by-step process of simplifying the algebraic expression (-3x^3+5x^2+10x+4)-(x^3+7x^2-3x+1). By distributing the negative sign and combining like terms, we arrived at the simplified expression -4x^3 - 2x^2 + 13x + 3.
