Question

The expression \[ a^{2} - 25 \] is first written as \[ a^{2} - 5^{2} \]. What is its factorisation?

Options

• \( (a - 5)(a - 5) \)

• \( (a - 5)(a + 5) \)

• \( (a + 5)(a + 5) \)

• \( (a - 25)(a + 1) \)

Answer 1

\[ a^{2} - 25 = a^{2} - 5^{2} = (a - 5)(a + 5) \]. This uses the difference of two squares, giving the two linear factors \( (a - 5) \) and \( (a + 5) \).