%2B(2a%5E3-5a%5E2%2B8).jpeg "(4a-a^3-3)+(2a^3-5a^2+8)")
Simplifying Algebraic Expressions
In mathematics, simplifying algebraic expressions involves combining like terms and performing operations to make the expression as concise as possible. Let's look at the expression (4a-a^3-3)+(2a^3-5a^2+8) and see how to simplify it.
Step 1: Remove the Parentheses
Since we are adding the two expressions, we can simply remove the parentheses:
4a - a^3 - 3 + 2a^3 - 5a^2 + 8
Step 2: Identify and Combine Like Terms
Like terms are terms that have the same variable and exponent. Let's identify and group the like terms in our expression:
- a^3 terms: -a^3 + 2a^3
- a^2 terms: -5a^2
- a terms: 4a
- Constant terms: -3 + 8
Now, combine the coefficients of the like terms:
- a^3 terms: (-1 + 2)a^3 = a^3
- a^2 terms: -5a^2
- a terms: 4a
- Constant terms: (-3 + 8) = 5
Step 3: Write the Simplified Expression
Finally, we combine all the simplified terms to get the simplified expression:
a^3 - 5a^2 + 4a + 5
Therefore, the simplified form of the expression (4a-a^3-3)+(2a^3-5a^2+8) is a^3 - 5a^2 + 4a + 5.