(a^3-2a^2)-(3a^2-4a^3) Simplified

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Jun 07, 2024

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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):

1. Evaluate the expressions inside the parentheses.
2. 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 and 3a^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.