Math worksheet with algebraic equations and solutions.

The image contains a series of algebraic expressions and equations, each labeled with a letter (e.g., A, B, C). The task appears to involve solving or simplifying these expressions. Below, I will solve and explain the solution for each expression.

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Expressions and Solutions

#### (A) \( 3x^2 + 5 \)
This is already in its simplest form. There are no like terms to combine, and no operations to perform.
Solution: \( 3x^2 + 5 \)

#### (B) \( 4x^2 - x - 6 \)
This is also in its simplest form. It is a quadratic expression with no like terms to combine.
Solution: \( 4x^2 - x - 6 \)

#### (C) \( x^2 - 4 \)
This is a difference of squares, which can be factored as:
\[ x^2 - 4 = (x - 2)(x + 2) \]
Solution: \( (x - 2)(x + 2) \)

#### (D) \( x^2 - x^2 \)
Simplify by combining like terms:
\[ x^2 - x^2 = 0 \]
Solution: \( 0 \)

#### (E) \( x \)
This is already in its simplest form.
Solution: \( x \)

#### (F) \( 6x - 3x^2 + 4x^2 - 2x \)
Combine like terms:
- Combine \( x^2 \)-terms: \( -3x^2 + 4x^2 = x^2 \)
- Combine \( x \)-terms: \( 6x - 2x = 4x \)
So, the expression simplifies to:
\[ x^2 + 4x \]
Solution: \( x^2 + 4x \)

#### (G) \( x + x^2 + x \)
Combine like terms:
- Combine \( x \)-terms: \( x + x = 2x \)
So, the expression simplifies to:
\[ x^2 + 2x \]
Solution: \( x^2 + 2x \)

#### (H) \( 4x^2 - x^2 - x \)
Combine like terms:
- Combine \( x^2 \)-terms: \( 4x^2 - x^2 = 3x^2 \)
So, the expression simplifies to:
\[ 3x^2 - x \]
Solution: \( 3x^2 - x \)

#### (I) \( x - x^2 \)
This is already in its simplest form.
Solution: \( x - x^2 \)

#### (J) \( x^2 + 3x^2 - 4x + 6x \)
Combine like terms:
- Combine \( x^2 \)-terms: \( x^2 + 3x^2 = 4x^2 \)
- Combine \( x \)-terms: \( -4x + 6x = 2x \)
So, the expression simplifies to:
\[ 4x^2 + 2x \]
Solution: \( 4x^2 + 2x \)

#### (K) \( 0 \)
This is already in its simplest form.
Solution: \( 0 \)

#### (L) \( x^2 - x^2 - x \)
Combine like terms:
- Combine \( x^2 \)-terms: \( x^2 - x^2 = 0 \)
So, the expression simplifies to:
\[ -x \]
Solution: \( -x \)

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Final Answer

\[
\boxed{
\begin{array}{ll}
\text{(A)} & 3x^2 + 5 \\
\text{(B)} & 4x^2 - x - 6 \\
\text{(C)} & (x - 2)(x + 2) \\
\text{(D)} & 0 \\
\text{(E)} & x \\
\text{(F)} & x^2 + 4x \\
\text{(G)} & x^2 + 2x \\
\text{(H)} & 3x^2 - x \\
\text{(I)} & x - x^2 \\
\text{(J)} & 4x^2 + 2x \\
\text{(K)} & 0 \\
\text{(L)} & -x \\
\end{array}
}
\]