Question

(i) 8x³ – y³ = (2x – y) (4x² + 2xy + y²)

(ii) 16x² – 9y² = (4x – 3y) (4x + 3y)

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

Let’s analyze each:

(i) 8x³ – y³:

We can rewrite (8x³) as (2x)³, so the expression becomes:

(2x)³ – y³

This fits the difference of cubes factorization formula:

a³ – b³ = (a – b)(a² + ab + b²)

Applying it here:

(2x – y)((2x)² + (2x)(y) + y²) = (2x – y)(4x² + 2xy + y²)

Which matches the given factorization for (i).

(ii) 16x² – 9y²:

This expression is a difference of squares, since:

16x² = (4x)²

9y² = (3y)²

So applying the difference of squares formula:

a² – b² = (a – b)(a + b)

We get:

(4x – 3y)(4x + 3y)

which matches the given statement (ii).

Therefore, both (i) and (ii) are correctly factorized.