If 9x\(^2\) + 6xy + 4y\(^2\) is a factor of 27x\(^3\) - 8y\(^3\), find the other factor.
2y + 3x
2y - 3x
3x + 2y
3x - 2y
Explanation
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27x³ - 8y³ = 3³x³ - 2³y³
= (3x)³ - (2y)³
= (3x - 2y) (9x² + 6xy + 4y²) (Difference of two cubes) i.e,
a³ - b³ = (a - b) (a² + ab + b²)
9x² + 6xy + 4y² is clearly a factor from what was given and also from our expansion of the difference of two cubes. Consequently, the other factor is (3x - 2y)
Please be writing the questions properly, the index appears to be whole number
27x^3 can be divided by 9x^2 which is = 3x
since there's a minus sign attached to 8y^3
-8y^3 can be divided by +4y^2 which is= -2y
3x-2y
to find out if I'm correct
multiply
(3x-2y)(3x-2y)
it will give u the factor of 27x^3-8y^3
from my own perspective or the way I think is the short method for this
we'll know that factors of a number are those number that can divide that number without remainder
so 27x^3can be divided by 3*
