Question

1/8 x3-1/27y3 please help ...factor ths expression completely, then place the factors in the proper location on the grid

Answer 1

factored form is:
`((x)/(2)-(y)/(3))((x^2)/(4)+(xy)/(6)+(y^2)/(9))`

Explanation:

The given expression is:

`(1)/(8)x^3 - (1)/(27)y^3`

The expression can be written as:

`((1)/(2)x)^3-((1)/(3)y)^3`

We know, a^3-b^3 = (a-b)(a^2+ab+b^2)

a= x/2 and b = y/3

Putting values in the formula given:

`((x)/(2)-(y)/(3))(((x)/(2))^2+((x)/(2))((y)/(3))+((y)/(3))^2)\\((x)/(2)-(y)/(3))((x^2)/(4)+(xy)/(6)+(y^2)/(9))`

So, factored form is:
`((x)/(2)-(y)/(3))((x^2)/(4)+(xy)/(6)+(y^2)/(9))`