Factorise :
`(a+b)^(2) - a^(2) + b^(2)`

Answer

To factorise the expression \((a+b)^{2} - a^{2} + b^{2}\), we can follow these steps:

### Step 1: Expand \((a+b)^{2}\)
Using the formula for the square of a binomial, we have:
\[ (a+b)^{2} = a^{2} + 2ab + b^{2} \]
So, we can rewrite the expression as:
\[ a^{2} + 2ab + b^{2} - a^{2} + b^{2} \]

### Step 2: Combine like terms
Now, we will combine the like terms in the expression:
\[ a^{2} - a^{2} + 2ab + b^{2} + b^{2} = 0 + 2ab + 2b^{2} = 2ab + 2b^{2} \]

### Step 3: Factor out the common term
In the expression \(2ab + 2b^{2}\), we can factor out \(2b\):
\[ 2b(a + b) \]

### Final Answer
Thus, the factorised form of the expression \((a+b)^{2} - a^{2} + b^{2}\) is:
\[ 2b(a + b) \]

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