Write the number of terms and also list out the terms in each of the following algebraic expressions.
`(2a) (-a) +(3b) b- (5c)c+(2a)a-(2b)(-b)`

Answer

To solve the problem, we will first simplify the given algebraic expression step by step and then identify the number of terms and list them out.

Given expression:
\[ (2a)(-a) + (3b)(b) - (5c)(c) + (2a)(a) - (2b)(-b) \]

**Step 1: Multiply the terms.**

1. **Multiply \( (2a)(-a) \)**:
\[ 2a \cdot -a = -2a^2 \]

2. **Multiply \( (3b)(b) \)**:
\[ 3b \cdot b = 3b^2 \]

3. **Multiply \( -(5c)(c) \)**:
\[ -5c \cdot c = -5c^2 \]

4. **Multiply \( (2a)(a) \)**:
\[ 2a \cdot a = 2a^2 \]

5. **Multiply \( -(2b)(-b) \)**:
\[ -2b \cdot -b = 2b^2 \]

Now, substituting these results back into the expression, we get:
\[ -2a^2 + 3b^2 - 5c^2 + 2a^2 + 2b^2 \]

**Step 2: Combine like terms.**

1. Combine the \( a^2 \) terms:
\[ -2a^2 + 2a^2 = 0 \]

2. Combine the \( b^2 \) terms:
\[ 3b^2 + 2b^2 = 5b^2 \]

3. The \( c^2 \) term remains:
\[ -5c^2 \]

Now, the expression simplifies to:
\[ 5b^2 - 5c^2 \]

**Step 3: Identify the number of terms and list them.**

The simplified expression \( 5b^2 - 5c^2 \) has 2 terms:
1. \( 5b^2 \)
2. \( -5c^2 \)

**Final Answer:**
- Number of terms: 2
- Terms: \( 5b^2, -5c^2 \)

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