(8a-4a^2)-(7a^3-a)

2 min read Jun 16, 2024

Simplifying the Expression (8a - 4a²) - (7a³ - a)

This article will guide you through simplifying the expression (8a - 4a²) - (7a³ - a).

Understanding the Expression

The expression involves polynomials, which are expressions consisting of variables and constants combined using addition, subtraction, and multiplication. The variables can be raised to various powers (exponents).

Simplifying the Expression

Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by -1.
```
(8a - 4a²) - (7a³ - a) = 8a - 4a² - 7a³ + a 
```
Combine like terms: Identify terms with the same variable and exponent. Combine their coefficients.
```
8a - 4a² - 7a³ + a = -7a³ - 4a² + (8a + a) 
```
```
= -7a³ - 4a² + 9a
```

Final Simplified Expression

The simplified form of the expression (8a - 4a²) - (7a³ - a) is -7a³ - 4a² + 9a.

Key Takeaways

Distributing negative signs is crucial when dealing with expressions involving parentheses.
Combining like terms simplifies the expression and makes it easier to work with.
Order of terms in the final expression is usually determined by descending order of exponents.