Factorise by grouping method :
`y^(2) - (a+b)y + ab`

Answer

To factorise the expression \( y^2 - (a+b)y + ab \) by the grouping method, we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ y^2 - (a+b)y + ab \]

### Step 2: Expand the middle term
We can rewrite the middle term \(-(a+b)y\) as \(-ay - by\):
\[ y^2 - ay - by + ab \]

### Step 3: Group the terms
Now, we will group the terms into two pairs:
\[ (y^2 - ay) + (-by + ab) \]

### Step 4: Factor out the common factors from each group
From the first group \(y^2 - ay\), we can factor out \(y\):
\[ y(y - a) \]
From the second group \(-by + ab\), we can factor out \(-b\):
\[ -b(y - a) \]

### Step 5: Combine the factored groups
Now, we can combine the two factored groups:
\[ y(y - a) - b(y - a) \]
Notice that \((y - a)\) is common in both terms.

### Step 6: Factor out the common binomial
Now we can factor out \((y - a)\):
\[ (y - a)(y - b) \]

### Final Result
Thus, the factorization of the expression \( y^2 - (a+b)y + ab \) is:
\[ (y - a)(y - b) \]

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