Question

Simplify (3x +y)whole cube - (3x - y ) whole cube

Answer 1

Answer:

54x^2y+2y^3

Step-by-step explanation:

(3x+y)^3-(3x-y)^3. [a^3-b^3=(a-b)(a^2+ab+b^2)]

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

(3x+y-3x+y)(9x^2+y^2+6xy+9x^2-y^2+9x^2+y^2-6xy)

(2y)(27x^2+y^2)

54x^2y+2y^3

Answer 2

According to the question, it is given that

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

We have to simplify the given expression,

As we know that the identity for

$[a^3-b^3=(a-b)(a^2+ab+b^2)]$

By substituting the given expression in the above identity:

So, we will get:  

$=>[(3x+y)-(3x-y)][(3x+y)^2+(3x+y)(3x-y)+(3x-y)^2]$

By simplifying it further we get:  

$=>(3x+y-3x+y)(9x^2+y^2+6xy+9x^2-y^2+9x^2+y^2-6xy)$

Cancelling out and adding the like terms the terms we get,

 $=>(2y)(27x^2+y^2)$

$=>54x^2y+2y^3$

Hence, by simplifying $(3x+y)^3-(3x-y)^3$ we get $54x^2y+2y^3$.