Question

Factorise (x+y)^3-x-y

Answer 1

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Answer 2

Answer:

Required factors are $(x + y) \: and \: ( {x}^{2} + {y}^{2} + 2xy - 1)$

Step-by-step explanation:

Given,${(x + y)}^{3} - x - y$

We want to factorise it.

Now,

${(x + y)}^{3} - (x + y) \\ = (x + y)(( {(x + y)}^{2} - 1)) \\ = (x + y)( {x}^{2} + {y}^{2} + 2xy - 1)$

After factorization,

The given term become

$(x + y)( {x}^{2} + {y}^{2} + 2xy - 1)$

Therefore, factors of given term are $(x + y) \: and \: ( {x}^{2} + {y}^{2} + 2xy - 1)$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

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2) https://brainly.in/question/1169549