Question
Factorise:
27x3 - y3 - z3 - 9xyz
27x3 - y3 - z3 - 9xyz
✓
Answer
27x3 - y3 - z3 - 9xyz
= (3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
We know,
a3 + b3 + c3 - 3abc
= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
a = 3x, b = -y, c = -z
(3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3xz)
= (3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
We know,
a3 + b3 + c3 - 3abc
= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
a = 3x, b = -y, c = -z
(3x)3 - y3 - z3 - 3 × (3x) × (-y) × (-z)
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3xz)
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