Answer:

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Step-by-step explanation:

Factorise the following: (i) x³ - y³ + 1 + 3x (ii) 2√2x³ +8y³-27z³ +18√2xyz

Answer:

(i) To factorize x³ - y³ + 1 + 3x, we can use the formula for the difference of cubes, which is a³ - b³ = (a - b)(a² + ab + b²).

The given expression can be written as:

x³ - y³ + 1 + 3x

Now, notice that we can write 1 as 1³ to make it a perfect cube:

x³ - y³ + 1³ + 3x

Using the difference of cubes formula, we get:

(x - y + 1)(x² + xy + 1) + 3x

(ii) To factorize 2√2x³ + 8y³ - 27z³ + 18√2xyz, we can observe that it is a sum of cubes.

The given expression can be written as:

2√2x³ + 8y³ - 27z³ + 18√2xyz

Now, notice that 2√2x³ can be written as (2√2x)³ and 8y³ can be written as (2y)³:

(2√2x)³ + (2y)³ - 27z³ + 18√2xyz

Using the sum of cubes formula, which is a³ + b³ = (a + b)(a² - ab + b²), we get:

[(2√2x + 2y)(4x - 2√2xy + 4y²)] - 27z³ + 18√2xyz

The final factorized expression is:

(2√2x + 2y)(4x - 2√2xy + 4y²) - 27z³ + 18√2xyz

Step-by-step explanation: