Question

Factorise:

64a³ + 125b³

Answer 1

To factorise, 64a³ + 125b³

Compare the expression with the algebraic identity a³ + b³ = (a + b)(a² – ab + b²)

We know that,

64 = 4³

125 = 5³

So, 64a³ + 125b³  = (4a)³ + (5b)³

Therefore, a = 4a, b = 5b

Hence, 64a³ + 125b³ = (4a + 5b) (16a² – 20ab + 25b²)