Simplify 2x^2+3y-2x+5y+2x

Solution:

Step 1: Identify like terms in the expression $2x^2+3y-2x+5y+2x$.

Step 1.1: Cancel out the terms $-2x$ and $2x$.

$2x^2+3y+5y+(2x-2x)$ $2x^2+3y+5y+0$

Step 1.2: Simplify the expression by removing the zero term.

$2x^2+3y+5y$

Step 2: Combine the like terms $3y$ and $5y$.

$2x^2+(3y+5y)$ $2x^2+8y$

Knowledge Notes:

To simplify an algebraic expression, you follow these steps:

1. Identify Like Terms: Like terms are terms that contain the same variables raised to the same power. In the given expression, $2x^2$, $-2x$, and $2x$ are like terms because they all contain the variable $x$. Similarly, $3y$ and $5y$ are like terms because they contain the variable $y$.

2. Combine Like Terms: This involves adding or subtracting coefficients of like terms. In the expression, $-2x$ and $2x$ cancel each other out because they are additive inverses, resulting in zero. When you add $3y$ and $5y$, you combine their coefficients to get $8y$.

3. Simplify the Expression: After combining like terms, you simplify the expression by removing any zero terms and writing the expression in a simplified form. In this case, the simplified expression is $2x^2+8y$.

Relevant algebraic properties used in simplification include the Commutative Property of Addition, which allows us to rearrange terms, and the Associative Property of Addition, which allows us to group terms in any order when adding. The concept of additive inverses is also used, where a number plus its negative equals zero.