please help in it is simple question ${x}^{2} - 4 \\ {x}^{3} - 27$

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please help in it is simple question
${x}^{2} - 4 \\ {x}^{3} - 27$

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Mathematics Neala 4 years 2021-07-19T23:39:39+00:00 2021-07-19T23:39:39+00:00 2 Answers 8 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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diemkieu · Answer 1 · 2021-07-19T23:41:18+00:00

diemkieu

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2021-07-19T23:41:18+00:00 July 19, 2021 at 11:41 pm

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1)

$\sf {x}^{2} - 4 \\ \sf \: Use \: the \: sum \: product \: method$

$\sf {x}^{2} - 4 \\ = \sf{x}^{2} + 2x - 2x - 4$

$\sf \: Now \: take \: the \: common \: factor \: out \\ \sf{x}^{2} + 2x - 2x - 4 \\\sf = x(x + 2) - 2(x + 2)$

$\sf \: Factorize \: it \\ \sf \: x(x + 2) - 2(x + 2) \\ = \sf(x - 2)(x + 2)$

Answer ⟶ $\boxed{\bf{(x-2)(x+2)}}$

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2)

$\sf {x}^{3} - 27$

$\sf {x}^{3} \: and \: 27 \: ( {3}^{3} ) \: are \: perfect \: real \: cubes.$

$\sf \: So \: use \: the \: algebraic \: identity \: \\ \sf {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

$\sf \: a = \sqrt[3]{x^{3}} = x \\ \sf \: b = \sqrt[3]{27} = 3$

$\sf \: {x}^{3} - {3}^{3} \\ \sf= (x - 3)( {x}^{2} + 3x + {3}^{2} ) \\ = \sf \: (x - 3)( {x}^{2} + 3x + 9)$

Answer ⟶ $\boxed{\bf{(x-3)(x^{2}+3x+9)}}$

Orla · Answer 2 · 2021-07-19T23:41:20+00:00

Orla

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2021-07-19T23:41:20+00:00 July 19, 2021 at 11:41 pm

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x^2 – 4 = (x-2) x (x + 2)
x^3 – 27 = (x-3) x (x^2+ 3x+9)