Question

Factorise.

x³ + 64y³

Answer 1

x³ + 64y³

= x³ + 4³y³

= x³ + (4y)³

We know that,

a³ + b³ = (a + b)(a² − ab + b²)

Here, a = x, b = 4y

∴ x³ + (4y)³ = (x + 4y)[x² − x × 4y + (4y)²]

= (x + 4y)[x² − 4xy + 4²y²]

= (x + 4y)(x² − 4xy + 16y²)

∴ x³ + 64y³ = (x + 4y)(x² − 4xy + 16y²)