Respuesta :

27=3³ and 512=8³
(3x+8y)(9x²-24xy+84y²) are the two factors. 
C is the answer. 

Option (C) [tex](9x^{2}-24xy+64y^{2} )[/tex] is one of the factors of [tex]27x^3 + 512y^3[/tex].

What is factorization?

Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

For the given situation,

The expression is [tex]27x^3 + 512y^3[/tex]

Here [tex]27=3^{3}[/tex] and [tex]512=8^{3}[/tex]

So, the expression can be rewrite as,

⇒ [tex](3x)^{3} +(8y)^{3}[/tex] ------- (1)

This expression is of the form,

[tex]a^{3} +b^{3}=(a+b)(a^{2}-ab+b^{2} )[/tex]

Here, a = 3x and b = 8y.

Then the expression 1 becomes,

⇒ [tex](3x)^{3} +(8y)^{3}=(3x+8y)((3x)^{2}-(3x)(8y)+(8y)^{2} )[/tex]

⇒ [tex](3x)^{3} +(8y)^{3}=(3x+8y)(9x^{2}-24xy+64y^{2} )[/tex]

Thus the factors are [tex](3x+8y)[/tex] and [tex](9x^{2}-24xy+64y^{2} )[/tex]

Hence we can conclude that option (C) [tex](9x^{2}-24xy+64y^{2} )[/tex] is one of the factors of [tex]27x^3 + 512y^3[/tex].

Learn more about factorization here

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