(w^3-3w^2+12w+8)+(2w^3-18w+4)

Jasonbradley

2 min read

·

Jun 16, 2024

29

Share

Simplifying Polynomial Expressions: A Step-by-Step Guide

In algebra, we often encounter expressions involving variables and their powers. These expressions can be simplified by combining like terms. Let's explore how to simplify the expression:

(w^3 - 3w^2 + 12w + 8) + (2w^3 - 18w + 4)

Step 1: Identify Like Terms

• Like terms have the same variable and exponent. For example, w^3 and 2w^3 are like terms, while w^3 and w^2 are not.

Let's identify the like terms in our expression:

• w^3 terms: w^3 and 2w^3
• w^2 terms: -3w^2 (there's no other w^2 term)
• w terms: 12w and -18w
• Constant terms: 8 and 4

Step 2: Combine Like Terms

Now we combine the coefficients of like terms:

• w^3 terms: w^3 + 2w^3 = 3w^3
• w^2 terms: -3w^2 (remains the same)
• w terms: 12w - 18w = -6w
• Constant terms: 8 + 4 = 12

Step 3: Write the Simplified Expression

Finally, we combine all the simplified terms:

**(w^3 - 3w^2 + 12w + 8) + (2w^3 - 18w + 4) = ** 3w^3 - 3w^2 - 6w + 12

Therefore, the simplified form of the given expression is 3w^3 - 3w^2 - 6w + 12.