Question

Find the factor of x + y cube minus x cube + y cube

Answer 1

Step-by-step explanation:

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Answer 2

The factors of $(x+y)^3-(x^3+y^3)$ are 1, 3 , x , y, xy ,  3x , 3y,  (x+y) , 3(x+y) , x(x+y) , y(x+y) ,(3xy) , (x+y)(3x) , (x+y)(3y) and  (x+y)(3xy).

Explanation:

The given expression : $(x+y)^3-(x^3+y^3)$

Using identity : $a^3+b^3=(a+b)(a^2-ab+b^2)$ , we get

$(x+y)^3-(x+y)(x^2-xy+y^2)$

Take (x+y) as common , we get

$(x+y)[(x+y)^2-(x^2-xy+y^2)]$

Using identity : $(a+b)^2=a^2+b^2+2ab$ , we get

$(x+y)[x^2+2xy+y^2-(x^2-xy+y^2)]$

$(x+y)[x^2+2xy+y^2-x^2+xy-y^2]$

$(x+y)[x^2-x^2+2xy+xy+y^2-y^2]$

$(x+y)(3xy)$

Factors of an expression are those expression that can divide the original expression.

Therefore , the factors of $(x+y)^3-(x^3+y^3)$ are 1 , 3 , x , y, xy , 3x , 3y,  (x+y) , 3(x+y) , x(x+y) , y(x+y) ,(3xy) , (x+y)(3x) , (x+y)(3y) and  (x+y)(3xy).

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