Questions: Simplify the algebraic expression by performing the indicated operations and combining the similar (or like) terms. 2(y^2+2y+2)-(y^2+3y+1)

Solution Steps

To simplify the given algebraic expression, we need to distribute the constants through the parentheses and then combine like terms.

1. Distribute the constants inside the parentheses.
2. Combine like terms by adding or subtracting the coefficients of similar terms.

First, distribute the constants inside the parentheses: \[ 2(y^2 + 2y + 2) - (y^2 + 3y + 1) \] This becomes: \[ 2y^2 + 4y + 4 - y^2 - 3y - 1 \]

Next, combine the like terms: \[ (2y^2 - y^2) + (4y - 3y) + (4 - 1) \] This simplifies to: \[ y^2 + y + 3 \]

Final Answer