Question

Factorise 27x3+y3+z3-9xyz
Verify x3+y3=(x+y)(x2-xy+y2

Answer 1

Answer:

1. x³ + y3 + z3 - 3xyz = (x + y + z)(x² + y² + z? - xy- yz zx)

= 27x3 + y3 + z3 – 9xyz = (3x)³ + y³ + z³ - 3(3x)(y)(z)

= (3x + y + z)(3x)² + y? + z² – 3xy - yz – 3xz

= (3x + y + z)(9x2 + y² + z² - 3xy – yz – 3xz)

2. x3−y3=(x−y)x2+(x−y)(xy)+(x−y)y2  

⟹x3−x2y+x2y−xy2+xy2−y3

⟹x3−y3

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