Question

Factorise using suitable formula: a^3 + 27b^3 + 64c^3 – 36abc . With a proper solution please.

Answer 1

Answer:

We know the identity a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

Using the above identity taking a=a,b=−b and c=2c, the equation a

3

−b

3

+8c

3

+6abc can be factorised as follows:

a

3

−b

3

+8c

3

+6abc=(a

3

)+(−b)

3

+(2c)

3

−3(a)(−b)(2c)

=[a+(−b)+(2c)][a

2

+(−b)

2

+(2c)

2

−(a×−b)−(−b×2c)−(2c×a)]

=(a−b+2c)(a

2

+b

2

+4c

2

+ab+2bc−2ca)

Answer 2

Step-by-step explanation:

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