Question

27 x cube + y cube + Z cube minus 9 xyz factorise​

Answer 1

Hey there !!

$\sf 27x{}{^3}+y{}^{3}+z{}^{3}-9xyz$

$\sf (3x){}^{3}+(y){}^{3}+(z){}^{3}= -3×(3x)×y×z$

a=3x, b=y, c=z

$\sf (a+b+c)(a{}^{2}+b{}^{2}+c{}^{2}-ab-bc-ca$

$\sf (3x+y+z)(3x{}^{2}+y{}^{2}+z{}^{2}-(3x×y)-(y×z)-(z×3x)</p><p>$

$\sf (3x+y+z)(9x{}^{2}+y{}^{2}+z{}^{2}-3xy-yz-3xz$

Hope it's help uh

Answer 2

SOLUTION

$= > 27 {x}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ = > (3x) {}^{3} + {y}^{3} + {z}^{3} - (3)(3x)(y)(z) \\ = > <strong>{a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)</strong> \\ = > (3x + y + z)</u><u>[</u><u>(3x) {}^{2} + {y}^{2} + {z}^{2} - (3x)(y) - (y)(z) - (z)(3x) </u><u>]</u><u>\\ = > ( 3x + y + z)(9 {x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz)$

hope it helps ☺️