The problem asks to simplify the algebraic expressions given in the image. I will solve problem number 12: $x^2 + 3x^2 - 4x^2 + 5x$.

1. Problem Description

The problem asks to simplify the algebraic expressions given in the image. I will solve problem number 12: $x^2 + 3x^2 - 4x^2 + 5x$.

2. Solution Steps

The problem requires combining like terms. Like terms are terms that have the same variable raised to the same power. In this problem, we have $x^2$ terms and an $x$ term.

First, we group the $x^2$ terms together:

$x^2 + 3x^2 - 4x^2$

We can simplify this by adding the coefficients of the $x^2$ terms:

$1x^2 + 3x^2 - 4x^2 = (1 + 3 - 4)x^2 = (4 - 4)x^2 = 0x^2 = 0$

Now, we combine the result with the remaining term $5x$:

$0 + 5x = 5x$

3. Final Answer

$5x$