Simplifying Algebraic Expressions: A Step-by-Step Guide
In this article, we will explore how to simplify the algebraic expression -3x^4 + 6x^3 - 11x^2 + 5 - (5x^4 + 2x^3 - x)
. We will break down the steps to combine like terms and simplify the expression.
Step 1: Distribute the Negative Sign
First, we need to distribute the negative sign to the terms inside the parentheses:
-3x^4 + 6x^3 - 11x^2 + 5 - 5x^4 - 2x^3 + x
Step 2: Combine Like Terms
Now, we will combine like terms:
x^4 terms: -3x^4 - 5x^4 = -8x^4
x^3 terms: 6x^3 - 2x^3 = 4x^3
x^2 terms: -11x^2
(no other x^2 terms to combine with)
x terms: x
(no other x terms to combine with)
Constant terms: 5
(no other constant terms to combine with)
Step 3: Write the Simplified Expression
Now, we can write the simplified expression:
-8x^4 + 4x^3 - 11x^2 + x + 5
And that's it! We have successfully simplified the algebraic expression -3x^4 + 6x^3 - 11x^2 + 5 - (5x^4 + 2x^3 - x)
.