(10x-x^2+8)+(5x^2+1-22x)

2 min read Jun 16, 2024

Simplifying Algebraic Expressions: (10x-x^2+8)+(5x^2+1-22x)

This article will guide you through the process of simplifying the algebraic expression: (10x-x^2+8)+(5x^2+1-22x).

Before we begin, let's remember a few key concepts:

Terms: Parts of an expression separated by addition or subtraction signs. For example, in the expression (10x-x^2+8), the terms are 10x, -x^2, and 8.
Like Terms: Terms that have the same variable and exponent. For instance, 10x and -22x are like terms because they both have 'x' to the power of 1.
Combining Like Terms: We can add or subtract coefficients of like terms. For example, 10x - 22x = -12x.

Remove the parentheses: Since we are adding the two expressions, the parentheses do not affect the order of operations.

(10x-x^2+8) + (5x^2+1-22x) = 10x - x^2 + 8 + 5x^2 + 1 - 22x
Identify Like Terms: Group the like terms together.

(10x - 22x) + (-x^2 + 5x^2) + (8 + 1)
Combine Like Terms: Combine the coefficients of each set of like terms.

-12x + 4x^2 + 9
Rearrange (Optional): It's often standard to write the terms in descending order of their exponents.

4x^2 - 12x + 9

The simplified form of the algebraic expression (10x-x^2+8)+(5x^2+1-22x) is 4x^2 - 12x + 9.