Question

Do the below sums:
i)8a³ +b³+27c³ - 18abc
ii)64a³+27b³+8c³-72abc
iii)125a³ +b³+64c³-60abc​

Answer 1

Answer:

Step-by-step explanation:

i) a3 + 8b3 - 27c2 + 18 abc

= (a)3 + (2b)3 + (-3c)3 + 18 abc

=(a)3 + (2b)3 + (-3c)3 - 3(a) (2b) (-3c)

We know that

x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

Therefore,

(a)3 + (2b)3 + (-3c)3 - 3(a) (2b) (-3c)

= (a + 2b - 3c) (2a2 + 4b2 + 9c2 - 2ab + 6bc + 3 ac)