Question

Factorise the following:

(x – 4) (x + 4) + 7

Answer 1

Given expression: (x – 4)(x + 4) + 7

Step-wise calculation:

1. Use the difference of squares formula:

(a – b)(a + b) = a² – b²

(x – 4)(x + 4) = x² – 16

2. Substitute back into the expression:

x² – 16 + 7 = x² – 9

3. Recognize that x² – 9 is a difference of squares: 

x² – 9 = (x – 3)(x + 3)