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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

User Dyane
by
7.3k points

1 Answer

4 votes

Answer:

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.

User Achille G
by
7.2k points