Factorise : `a^(3) -b^(3)+ 4(a-b)`

Answer

To factorise the expression \( a^3 - b^3 + 4(a - b) \), we can follow these steps:

### Step 1: Identify the difference of cubes
We recognize that \( a^3 - b^3 \) can be factored using the formula for the difference of cubes:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]

### Step 2: Rewrite the expression
We can rewrite the original expression by substituting the factored form of \( a^3 - b^3 \):
\[ a^3 - b^3 + 4(a - b) = (a - b)(a^2 + ab + b^2) + 4(a - b) \]

### Step 3: Factor out the common term
Now, we notice that \( (a - b) \) is a common factor in both terms:
\[ = (a - b)(a^2 + ab + b^2 + 4) \]

### Step 4: Write the final factored form
Thus, the final factored form of the expression is:
\[ (a - b)(a^2 + ab + b^2 + 4) \]

### Summary
The expression \( a^3 - b^3 + 4(a - b) \) can be factorised as:
\[ (a - b)(a^2 + ab + b^2 + 4) \]