factor completely
27x^2y+90xy^2+75y^3
3y ( 9 x^2 +30 x y + 25 y^2)
3 y (3 x + 5 y)(3 x + 5 y)
To factor the expression 27x^2y + 90xy^2 + 75y^3 completely, we need to look for any common factors among the terms.
Step 1: Find the Greatest Common Factor (GCF) of the terms.
The GCF of 27, 90, and 75 is 3. The GCF of x, x, and y is xy. The GCF of y^2 and y^3 is y^2.
Step 2: Divide each term by the GCF.
Dividing 27x^2y by 3xy gives us 9x.
Dividing 90xy^2 by 3xy gives us 30y.
Dividing 75y^3 by 3xy^2 gives us 25y.
Now, the factored expression is 3xy(9x + 30y + 25y^2).
Therefore, the expression 27x^2y + 90xy^2 + 75y^3 can be factored completely as 3xy(9x + 30y + 25y^2).