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Q: How do you factor 64x to the third power minus 27y to the third power?

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Reorder the terms: -5 + 42y + 27y2 Factor a trinomial. (-5 + -3y)(1 + -9y)

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n=72 satisfies the relation. 2*72 = 12**2, and 3*72 = 6**3. The only question is whether or not that is the smallest integer that will do so. All perfect squares of which 2n is a factor are of form (2x)**2 = 4x**2, with n= 2x**2. Similarly all perfect cubes of which 3n is a factor are of form (3y)**3 = 27y**3 with n = 9y**3. So, we need integers x and y such that 2x**2 = 9y**3. If the integers x and y are the smallest that satisfy the equation, then we have the smallest n. It doesn't work for y = 1, or any other odd number. If y = 2, n = 72. There is a number x =6 which satisfies the relation. Since y is smallest possible, then n=72 is the smallest positive integer that satisfies the relation.

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In case you meant 64x^3 - 27y^3, that factors to (4x - 3y)(16x^2 + 12xy + 9y^2)

Since 27y is a factor of 54y3, it is automatically the GCF.

Since 27y is a factor of 54y3, it is automatically the GCF

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It is: 3y and y

9(x - 3y)

(y + 27)(y^2 - 27y + 729)

Since 54y3 is a multiple of 27y, it is automatically the LCM.

189xy

Reorder the terms: -5 + 42y + 27y2 Factor a trinomial. (-5 + -3y)(1 + -9y)

It depends on where there are parentheses, if there are any. y + 33 + 2/4 = y + 27.5 (y+3)3 + 2/4 = y3 + 9y2 + 27y + 27.5

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