Question

Factorise x²-5 please

Answer 1

$\sf \: {x}^{2} - 5$

$\sf \: Use \: the \: algebraic \: identity \\ \sf \: a {}^{2} - {b}^{2} = (a - b)(a + b)$

$\sf \: Substitute \: the \: value \: of \: a \: and \: b \: in \: the \: identity.$

$\sf \: a = \sqrt{x ^{2} } = x \\ \sf \: b = \sqrt{5}$

$\sf \: the \: identity \: becomes \:$

$\sf {x}^{2} - 5 \\ \sf = (x - \sqrt{5} )(x + \sqrt{5} )$

Answer ⟶ $\boxed{\bf{(x - \sqrt{5} )(x + \sqrt{5} )}}$