Simplifying Algebraic Expressions: (a^3-2a^2)-(3a^2-4a^3)
When working with algebraic expressions, simplifying them is an essential step in understanding and solving equations. In this article, we will explore how to simplify the expression (a^3-2a^2)-(3a^2-4a^3)
.
Step 1: Follow the Order of Operations
To simplify this expression, we need to follow the order of operations (PEMDAS):
- Evaluate the expressions inside the parentheses.
- Combine like terms.
Step 2: Evaluate the Expressions Inside the Parentheses
Let's evaluate the expressions inside the parentheses:
(a^3-2a^2)
= a^3 - 2a^2
(3a^2-4a^3)
= 3a^2 - 4a^3
Now, we can rewrite the original expression as:
(a^3 - 2a^2) - (3a^2 - 4a^3)
Step 3: Combine Like Terms
To combine like terms, we need to identify the terms with the same variable and exponent:
a^3
:a^3
and-4a^3
have the same variable and exponent, so we can combine them:a^3 - 4a^3 = -3a^3
a^2
:-2a^2
and3a^2
have the same variable and exponent, so we can combine them:-2a^2 + 3a^2 = a^2
Now, we can rewrite the expression as:
-3a^3 + a^2
Simplified Expression
The simplified expression is:
-3a^3 + a^2
By following the order of operations and combining like terms, we have successfully simplified the expression (a^3-2a^2)-(3a^2-4a^3)
to -3a^3 + a^2
.