Factorise :
`(a^(2) - 3a)(a^(2) - 3a + 7) + 10`

Answer

To factorise the expression \((a^2 - 3a)(a^2 - 3a + 7) + 10\), we can follow these steps:

### Step 1: Substitute
Let \( t = a^2 - 3a \). Then the expression becomes:
\[ t(t + 7) + 10 \]

### Step 2: Expand the Expression
Now, expand the expression:
\[ t(t + 7) + 10 = t^2 + 7t + 10 \]

### Step 3: Factor the Quadratic
Next, we need to factor the quadratic \( t^2 + 7t + 10 \). We look for two numbers that multiply to \( 10 \) (the constant term) and add to \( 7 \) (the coefficient of \( t \)). The numbers \( 5 \) and \( 2 \) satisfy this condition:
\[ t^2 + 7t + 10 = (t + 5)(t + 2) \]

### Step 4: Substitute Back
Now, substitute back \( t = a^2 - 3a \):
\[ (a^2 - 3a + 5)(a^2 - 3a + 2) \]

### Step 5: Final Expression
Thus, the factorised form of the original expression is:
\[ (a^2 - 3a + 5)(a^2 - 3a + 2) \]