-(4-2x)%2B(5x%5E2%2B7).jpeg "(3x^2+5x+2)-(4-2x)+(5x^2+7)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
In this article, we will explore how to simplify the algebraic expression: (3x^2 + 5x + 2) - (4 - 2x) + (5x^2 + 7)
Step 1: Distributing the Negative Sign
The expression contains parentheses, indicating that we need to distribute the negative sign before simplifying further.
- (3x^2 + 5x + 2) - (4 - 2x) + (5x^2 + 7)
- 3x^2 + 5x + 2 - 4 + 2x + 5x^2 + 7
Step 2: Combining Like Terms
Now that the parentheses are removed, we can combine terms with the same variable and exponent.
- 3x^2 + 5x^2 + 5x + 2x + 2 - 4 + 7
Step 3: Simplifying
Finally, we can simplify the expression by adding and subtracting the coefficients.
- 8x^2 + 7x + 5
Final Result
Therefore, the simplified form of the algebraic expression (3x^2 + 5x + 2) - (4 - 2x) + (5x^2 + 7) is 8x^2 + 7x + 5.
Key Takeaways
- Distribute the negative sign: When removing parentheses preceded by a negative sign, remember to change the sign of each term inside the parentheses.
- Combine like terms: Group together terms with the same variable and exponent.
- Simplify: Perform the necessary addition and subtraction to arrive at the simplest form of the expression.
This step-by-step process allows us to systematically simplify complex algebraic expressions, leading to a clear and concise representation.