Factorise the expression `a ^(3) b ^(2) + a ^(2) b ^(3)`

Options

A. `a ^(2) b ^(2) (a +b)`
B. `ab (ab + ab)`
C. `ab (a +b)`
D. `a ^(3) b ^(3)`

Answer

To factorize the expression \( a^3 b^2 + a^2 b^3 \), follow these steps:

### Step 1: Identify Common Factors
Look for the common factors in both terms of the expression. The terms are \( a^3 b^2 \) and \( a^2 b^3 \).

### Step 2: Factor Out the Common Terms
The common factors in both terms are \( a^2 \) and \( b^2 \). So we can factor out \( a^2 b^2 \) from the expression.

\[ a^3 b^2 + a^2 b^3 = a^2 b^2 (a + b) \]

### Step 3: Write the Final Factored Form
After factoring out the common terms, the expression can be rewritten as:

\[ a^2 b^2 (a + b) \]

### Final Answer
The factored form of the expression \( a^3 b^2 + a^2 b^3 \) is:

\[ a^2 b^2 (a + b) \]

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