**(i) (a + b) ^{3} – a – b**

**(ii) x ^{2} – 2xy + y^{2} – a^{2} – 2ab – b^{2}**

**Answer:**

**(i) (a + b)**^{3} – a – b

^{3}– a – b

Above terms can be written as,

(a + b)^{3} – (a + b)

Take out common in all terms,

(a + b) [(a + b)^{2} – 1]

(a + b) [(a + b)^{2} – 1^{2}]

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

(a + b) (a + b + 1) (a + b – 1)

**(ii) x**^{2} – 2xy + y^{2} – a^{2} – 2ab – b^{2}

^{2}– 2xy + y

^{2}– a

^{2}– 2ab – b

^{2}

x^{2} – 2xy + y^{2} – a^{2} – 2ab – b^{2}

Above terms can be written as,

(x^{2} – 2xy + y^{2}) – (a^{2} + 2ab + b^{2})

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

(x^{2} – (2 × x × y) + y^{2}) – (a^{2} + (2 × a × b) + b^{2})

(x – y)^{2} – (a + b)^{2}

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

[(x – y) + (a + b)] [(x – y) – (a + b)]

(x – y + a + b) (x – y – a – b)

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