Write the number of terms and also list out the terms in each of the following algebraic expressions.
`(2xy) y+(4y)+z^2-x(2y^2)`

Answer

To solve the problem, we need to analyze the given algebraic expression step by step.

### Given Expression:
\[ (2xy) y + (4y) + z^2 - x(2y^2) \]

### Step 1: Expand the Expression
First, we will expand the expression where necessary.

1. The term \((2xy) y\) can be simplified:
\[ 2xy \cdot y = 2xy^2 \]

2. The term \(-x(2y^2)\) can also be simplified:
\[ -x(2y^2) = -2xy^2 \]

Now, substituting these simplifications back into the expression gives us:
\[ 2xy^2 + 4y + z^2 - 2xy^2 \]

### Step 2: Combine Like Terms
Next, we will combine the like terms in the expression:
- The terms \(2xy^2\) and \(-2xy^2\) will cancel each other out.

Thus, we are left with:
\[ 4y + z^2 \]

### Step 3: Identify the Terms
Now, we can identify the terms in the simplified expression \(4y + z^2\).

- The first term is \(4y\).
- The second term is \(z^2\).

### Step 4: Count the Number of Terms
Now, we count the number of terms:
- There are **2 terms** in total.

### Final Answer:
- **Number of Terms**: 2
- **Terms**: \(4y\) and \(z^2\)

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