Question

x³ + 27y³ is equal to ______.

Options

• (x + 3y)³

• (x + 3y) (x² – 6xy + 9y²)

• (x + 3y) (x² – 3xy + 9y²)

• (x + 3y) (x² + 3xy + 9y²)

Answer 1

x³ + 27y³ is equal to (x + 3y) (x² – 3xy + 9y²).

Explanation:

We are asked to factorise x³ + 27y³.

Step 1: Recognize it as a sum of cubes

x³ + 27y³ = x³ + (3y)³

Step 2: Apply the sum of cubes formula

The formula is a³ + b³ = (a + b)(a² – ab + b²)

Here, a = x and b = 3y:

x³ + (3y)³ = (x + 3y) (x² – x · 3y + (3y)²)

= (x + 3y) (x² – 3xy + 9y²)