Sure, let's solve the problem step by step:
Given the polynomial expression to simplify:
[tex]\[
(15x^3 + 10x^2 - 5x) + (5x)
\][/tex]
Step 1: Distribute and combine like terms.
- The original polynomial is [tex]\(15x^3 + 10x^2 - 5x\)[/tex].
- We need to add [tex]\(5x\)[/tex] to the polynomial.
Step 2: Identify and combine the like terms.
- The like terms in this expression are the terms that have the same power of [tex]\(x\)[/tex].
- In this case, [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] are like terms.
Step 3: Perform the addition of the like terms.
- Combine [tex]\(-5x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[
-5x + 5x = 0
\][/tex]
Step 4: Add the remaining terms of the polynomial.
- Since [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] cancel each other out, we are left with:
[tex]\[
15x^3 + 10x^2
\][/tex]
So, the simplified form of the given polynomial expression is:
[tex]\[
15x^3 + 10x^2
\][/tex]
