Question

How do you find the sum of cube ?

Answer 1

`(2x+5)(4x^(2) -10x+25)=0`

Explanation:

Given:

The given equation is.

`8x^(3) +125=0`

Find the some of cube.

Solution:

`8x^(3) +125=0`

`2^(3)x^(3) +5^(3)=0`

`(2x)^(3) +5^(3)=0`----------(1)

The sum of the cube formula is given below.

`(a^(3) +b^(3))=(a+b)(a^(2) -ab+b^(2) )`-----------(2)

By comparing equation 1 and equation 2

`a=2x, b=5`

substitute a and b value in equation 2

`((2x)^(3) +5^(3))=(2x+5)((2x)^(2) -(2x)(5)+5^(2))`

`((2x)^(3) +5^(3))=(2x+5)(4x^(2) -(10x)+25)`

`((2x)^(3) +5^(3))=(2x+5)(4x^(2) -10x+25)`

Therefore the sum of the cube
`(2x+5)(4x^(2) -10x+25)=0`