Question

1. a³ +27b³+8 c³ - 18 abc​

Answer 1

Answer:

Step-by-step explanation:

Put this in the form

a  

3

+(3b)  

3

+(2c)  

3

−3a(3b)(2c)

Use the familiar factorisation to get

a  

3

+27b  

3

+8c  

3

−18abc=(a+3b+2c)[a  

2

+(3b)  

2

+(2c)  

2

−a(3b)−3b(2c)−(2c)a]

Now simplify and get

a  

3

+27b  

3

+8c  

3

−18abc=(a+3b+2c)(a  

2

+9b  

2

+4c  

2

−3ab−6bc−2ca)

Answer 2

Answer:

a³+27b³+8c³-18abc

=a³+(3b)³+(2c)³-3×a×(3b)×(2c)

x³+y³+z³-3xyz, where a=x, 3b=y, 2c=z

(x+y+z)(x²+y²+z²-xy-yz-xz)

(a+3b+2c)(a²+9b²+4c²-3ab-6bc-2ca)