1)
[tex]\sf {x}^{2} - 4 \\ \sf \: Use \: the \: sum \: product \: method[/tex]
[tex]\sf {x}^{2} - 4 \\ = \sf{x}^{2} + 2x - 2x - 4[/tex]
[tex]\sf \: Now \: take \: the \: common \: factor \: out \\ \sf{x}^{2} + 2x - 2x - 4 \\\sf = x(x + 2) - 2(x + 2)[/tex]
[tex]\sf \: Factorize \: it \\ \sf \: x(x + 2) - 2(x + 2) \\ = \sf(x - 2)(x + 2)[/tex]
Answer ⟶ [tex]\boxed{\bf{(x-2)(x+2)}}[/tex]
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2)
[tex]\sf {x}^{3} - 27[/tex]
[tex]\sf {x}^{3} \: and \: 27 \: ( {3}^{3} ) \: are \: perfect \: real \: cubes.[/tex]
[tex]\sf \: So \: use \: the \: algebraic \: identity \: \\ \sf {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
[tex]\sf \: a = \sqrt[3]{x^{3}} = x \\ \sf \: b = \sqrt[3]{27} = 3[/tex]
[tex] \sf \: {x}^{3} - {3}^{3} \\ \sf= (x - 3)( {x}^{2} + 3x + {3}^{2} ) \\ = \sf \: (x - 3)( {x}^{2} + 3x + 9)[/tex]
Answer ⟶ [tex]\boxed{\bf{(x-3)(x^{2}+3x+9)}}[/tex]
