Question

Which of the following is a factor of 27x^3 – 64y3?

3x + 8y

9x^2 + 12xy + 16y^2

9x^2 + 24xy + 16y^2

None of the above

Answer 1

Which of the following is a factor of 27x^3 – 64y^3?
****

Answer 2

(3x-8y){(3x)^2 + (3x)(8y) + (8y)^2}

Answer 3

\[x^3-y^3=(x-y)(x^2+xy+y^2) \]

Answer 4

nathematicalpro.... none of the above right?

Answer 5

because 8^2 = 64

Answer 6

9x^2 + 12xy + 16y^2

Answer 7

27x^3 - 64y^3
= (3x}^3 - (4y)^3
= [ 3x - 4y ][ (3x)^2 + (3x)(4y) + (4y)^2 ] // since a^3-b^3 = (a-b)(a^2+ab+b^2)
= ( 3x - 4y )( 9x^2 + 12xy + 16y^2 )
therefore 9x^2 + 12xy + 16y^2 is a factor of 27x^3 – 64y3