Factorise :
`3-a(4+7a)`

Answer

To factorise the expression \( 3 - a(4 + 7a) \), we will follow these steps:

### Step 1: Distribute the negative sign and simplify
Start by distributing \( -a \) into the parentheses \( (4 + 7a) \):
\[ 3 - a(4 + 7a) = 3 - (4a + 7a^2) \]
This simplifies to:
\[ 3 - 4a - 7a^2 \]

### Step 2: Rearrange the expression
Rearranging the terms gives us:
\[ -7a^2 - 4a + 3 \]

### Step 3: Factor out the negative sign
To make factoring easier, we can factor out \(-1\):
\[ -(7a^2 + 4a - 3) \]

### Step 4: Factor the quadratic expression
Now we need to factor the quadratic \( 7a^2 + 4a - 3 \). We look for two numbers that multiply to \( 7 \times -3 = -21 \) and add to \( 4 \). The numbers \( 7 \) and \( -3 \) work because:
\[ 7 \times -3 = -21 \quad \text{and} \quad 7 + (-3) = 4 \]

### Step 5: Rewrite the middle term
We can rewrite \( 7a^2 + 4a - 3 \) as:
\[ 7a^2 + 7a - 3a - 3 \]

### Step 6: Group the terms
Now, we group the terms:
\[ (7a^2 + 7a) + (-3a - 3) \]

### Step 7: Factor by grouping
Now we factor out the common factors from each group:
\[ 7a(a + 1) - 3(a + 1) \]

### Step 8: Factor out the common binomial
Now we can factor out the common binomial \( (a + 1) \):
\[ (7a - 3)(a + 1) \]

### Step 9: Combine with the negative sign
Finally, we include the negative sign we factored out earlier:
\[ -(7a - 3)(a + 1) \]

### Final Answer
Thus, the factorised form of the expression \( 3 - a(4 + 7a) \) is:
\[ -(7a - 3)(a + 1) \]

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