Question

factorise (x+y) ³ - x-y ​

Answer 1

Answer:

(x + y)(x + y + 1)(x + y - 1)

Step-by-step explanation:

Given : (x + y)³ - x - y

We can write this as :

→ (x + y)³ - (x + y)

Taking common term (x + y) out.

→ (x + y) [ (x + y)² - 1 ]

We can write this as :

→ (x + y) [ (x + y)² - (1)² ]

• { Identity : a² - b² = (a + b)(a - b)

Here, a = (x + y), b = 1 }

→ (x + y) [ (x + y + 1)(x + y - 1) ]

→ (x + y)(x + y + 1)(x + y - 1)

Other identities which are frequently used :

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• (a + b)² - (a - b)² = 4ab

Answer 2

Answer:

(x + y)3 – x – y

= (x + y)3 – (x + y)

= (x + y) [(x + y)2 – 1] [Taking (x + y) common]

= (x + y) [(x + y)2 – (1)2]

= (x + y) [(x + y + 1) (x + y – 1)]

= (x + y) (x + y + 1) (x + y – 1)

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