Question

factorise
$\rm \: {27x}^{3}+ {y}^{3} + {z}^{3} -9xyz$
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Answer 1

Factorise

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

$\sf \longrightarrow {3x}^{3} + {y}^{3} + {z}^{3} - 3 \times 3x \times y \times z$

$\sf \longrightarrow (3x + y + z) [{(3x)}^{3} + {y}^{2} + {z}^{2} - 3xyz - yz - z \times 3x ]$

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

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@ShiningBlossom

Answer 2

Answer:

27x3+y3+z3−9xyz

\sf \longrightarrow {3x}^{3} + {y}^{3} + {z}^{3} - 3 \times 3x \times y \times z⟶3x3+y3+z3−3×3x×y×z

\sf \longrightarrow (3x + y + z) [{(3x)}^{3} + {y}^{2} + {z}^{2} - 3xyz - yz - z \times 3x ]⟶(3x+y+z)[(3x)3+y2+z2−3xyz−yz−z×3x]

\sf \longrightarrow (3x + y + z)( {9x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz)⟶(3x+y+z)(9x2+y2+z2−3xy−yz−3xz)

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