#### (i) 27x^{3}y^{3} – 8

Above terms can be written as,

(3xy)^{3} – 2^{3}

We know that, a^{3} – b^{3} = (a – b) (a^{2} + ab + b^{2})

Where, a = 3xy, b = 2

= (3xy – 2) ((3xy)^{2} + (3xy × 2) + 2^{2})

= (3xy – 2) (9x^{2}y^{2} + 6xy + 4)

##### (ii) 27(x + y)^{3} + 8(2x – y)^{3}

Above terms can be written as,

3^{3}(x + y)^{3} + 2^{3}(2x – y)^{3}

(3(x + y))^{3} + (2(x – y))^{3}

We know that, a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2})

Where, a = 3(x + y), b = 2(x – y)

= [3(x + y) + 2(2x – y)] [(3(x + y))^{3} – (3(x + y) × 2(2x – y)) + (2(2x – y))^{2}]

= [3x + 3y + 4x – 2y] [9(x + y)^{2} – 6(x + y)(2x – y) + 4(2x – y)^{2}]

= (7x – y) [9(x^{2} + y^{2} + 2xy) – 6(2x^{2} – xy + 2xy – y^{2}) + 4(4x^{2} + y^{2} – 4xy)]

= (7x – y) [9x^{2} + 9y^{2} + 18xy – 12x^{2} – 6xy – 6y^{2} + 16x^{2} + 4y^{2} – 16xy]

= (7x – y) [13x^{2} – 4xy + 19y^{2}]

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