hello and thanks ahead for helping,
i am not sure how to approach this problem, with trinom factoring? or the quadratic formula?, thanks!
Factor the following:
9 x^4 y^2-12 x^3 y^3+4 x^2 y^4
Factor x^2 y^2 out of 9 x^4 y^2-12 x^3 y^3+4 x^2 y^4:
x^2 y^2 (9 x^2-12 x y+4 y^2)
The coefficient of x^2 is 9 and the coefficient of y^2 is 4. The product of 9 and 4 is 36. The factors of 36 which sum to -12 are -6 and -6. So 9 x^2-12 x y+4 y^2 = 9 x^2-6 x y-6 x y+4 y^2 = 3 x (3 x-2 y)-2 (3 x-2 y) y:
x^2 y^2 3 x (3 x-2 y)-2 y (3 x-2 y)
Factor 3 x-2 y from 3 x (3 x-2 y)-2 y (3 x-2 y):
x^2 y^2 (3 x-2 y) (3 x-2 y)
(3 x-2 y) (3 x-2 y) = (3 x-2 y)^2:
Answer: |
| x^2 y^2 (3x - 2y)^2
+130536 9x^4 y^2 - 12x^3 y^3 + 4x^2 y^4 take out the greatest common factor, first
x^2 y^2 ( 9x^2 - 12xy + 4y^2) factor the expression in the parentheses
x^2 y^2 ( 3x - 2y) (3x - 2y) =
x^2 y^2 (3x - 2y) ^2
And that's it !!!
Factor the following:
9 x^4 y^2-12 x^3 y^3+4 x^2 y^4
Factor x^2 y^2 out of 9 x^4 y^2-12 x^3 y^3+4 x^2 y^4:
x^2 y^2 (9 x^2-12 x y+4 y^2)
The coefficient of x^2 is 9 and the coefficient of y^2 is 4. The product of 9 and 4 is 36. The factors of 36 which sum to -12 are -6 and -6. So 9 x^2-12 x y+4 y^2 = 9 x^2-6 x y-6 x y+4 y^2 = 3 x (3 x-2 y)-2 (3 x-2 y) y:
x^2 y^2 3 x (3 x-2 y)-2 y (3 x-2 y)
Factor 3 x-2 y from 3 x (3 x-2 y)-2 y (3 x-2 y):
x^2 y^2 (3 x-2 y) (3 x-2 y)
(3 x-2 y) (3 x-2 y) = (3 x-2 y)^2:
Answer: |
| x^2 y^2 (3x - 2y)^2
