Question

Factorise: 64a3 – 27b 3 – 144a2 b + 108ab2​

Answer 1

Answer:

= (4a)3 – (3b)3 – 3 (4a)2 (3b) + 3 (4a) (3b)2

= (4a – 3b)3

= (4a – 3b) (4a – 3b) (4a – 3b)

Answer 2

The given expression 64a

3

−27b

3

−144a

2

b+108ab

2

can be rewritten as:

64a

3

−27b

3

−144a

2

b+108ab

2

=(4a)

3

−(3b)

3

−(3×(4a)

2

×3b)+(3×4a×(3b)

2

)

=(4a−3b)

3

(∵(x−y)

3

=x

3

−y

3

−3x

2

y+3xy

2

)

Hence, 64a

3

−27b

3

−144a

2

b+108ab

2

=(4a−3b)

3

.