Fractorise:
`(x +y)(2x +5) - (x + y) (x +3)`

Answer

To factorise the expression \((x + y)(2x + 5) - (x + y)(x + 3)\), we can follow these steps:

### Step 1: Identify the common factor
Notice that both terms in the expression share a common factor of \((x + y)\).

### Step 2: Factor out the common term
We can factor out \((x + y)\) from both terms:

\[ (x + y)((2x + 5) - (x + 3)) \]

### Step 3: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:

\[ (2x + 5) - (x + 3) = 2x + 5 - x - 3 \]

Combine like terms:

\[ 2x - x + 5 - 3 = x + 2 \]

### Step 4: Write the final factored form
Now, substitute back into the factored expression:

\[ (x + y)(x + 2) \]

Thus, the final factored form of the expression is:

\[ \boxed{(x + y)(x + 2)} \]

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