Question

Choose one of the factors of 500x3 + 108y18

(500x to the 3rd + 108y to the 18th)

A. 25x2 + 15xy6 + 9y2
B. 5x + 3y6
C. All of the above
D. 6

Answer 1

The correct option is B.

Explanation:

The given expression is

`500x^3+108y^(18)`

Take out 4 as a common factor.

`500x^3+108y^(18)=4* (125x^3+27(y^6)^3)`

`500x^3+108y^(18)=4* (5^3x^3+3^3(y^6)^3)`

`500x^3+108y^(18)=4* ((5x)^3+(3y^6)^3)`

Use the formula
`a^3+b^3=(a+b)(a^2-ab+b^2)`,

Here
`a=5x` and
`b=3y^6`

`500x^3+108y^(18)=4* (5x+3y^6)((5x)^2-(5x)(3y^6)+(3y^6)^2)`

`500x^3+108y^(18)=4* (5x+3y^6)(25x^2-15xy^6+9y^(12))`

The factors of given expression are 4,
`(5x+3y^6)` and
`(25x^2-15xy^6+9y^(12))`.

Therefore only option B is correct.