Respuesta :

Thank you for posting your question here. Among the choice provided above the the factors of 27x3 512y3 is 9x2 − 24xy + 64y2. Factoring is finding what to multiply together to get an expression, it is somewhat the sames with splitting an expression into a multiplication of simpler expression.

Answer with explanation:

Factor of :

   [tex]27 x^3\pm 512 y^3\\\\= (3 x)^3 \pm(8 y)^3\\\\1.(3 x)^3+ (8 y)^3=(3 x + 8 y)[(3 x)^2-(3 x)(8y)+(8y)^2]\\\\ (3 x)^3+ (8 y)^3=(3 x + 8 y)[9 x^2-24 x y+64 y^2]\\\\2.(3 x)^3- (8 y)^3=(3 x - 8 y)[(3 x)^2+(3 x)(8y)+(8y)^2]\\\\ (3 x)^3- (8 y)^3=(3 x - 8 y)[9 x^2+24 x y+64 y^2][/tex]

Using the identity

[tex]1.a^3+b^3=(a+b)(a^2-ab+b^2)\\\\2. a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

So,

[tex](3 x)^3- (8 y)^3 {\text{has factor}} (3 x -8 y) and [9 x^2+24 x y+64 y^2], {\text{while}}, (3 x)^3+ (8 y)^3 {\text{has factor}} (3 x +8 y) and [9 x^2-24 x y+64 y^2],[/tex]

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