Assertion(A): $a^3 - 2\sqrt{2}b^3$ can be factorized as $(a - 2\sqrt{2})(a^2 + \sqrt{2}ab + 2b^2)$

Reason(R): x³ - y³ = (x - y)(x² + xy + y²).

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Given,

$a^3 - 2\sqrt{2}b^3$

By using identity,

a³ - b³ = (a - b)(a² + ab + b²)

$\Rightarrow (a)^3 - (\sqrt{2}b)^3 \\[1em] \Rightarrow (a - \sqrt{2}b)(a^2 + a(\sqrt{2}b) + (\sqrt{2}b)^2) \\[1em] \Rightarrow (a - \sqrt{2}b)(a^2 + \sqrt{2}ab + 2b^2) \\[1em]$

Assertion (A) is false.

Given,

x³ - y³ = (x - y)(x² + xy + y²)

This is a identity.

Reason (R) is true.

A is false, R is true.

Hence, option 2 is correct option.