Answer:
4 (3 y + 2 x)^2
Explanation:
Factor the following:
36 y^2 + 48 x y + 16 x^2
Hint: | Factor out the greatest common divisor of the coefficients of 36 y^2 + 48 x y + 16 x^2.
Factor 4 out of 36 y^2 + 48 x y + 16 x^2:
4 (9 y^2 + 12 x y + 4 x^2)
Hint: | Factor by grouping.
The coefficient of x^2 is 4 and the coefficient of y^2 is 9. The product of 4 and 9 is 36. The factors of 36 which sum to 12 are 6 and 6. So 9 y^2 + 12 x y + 4 x^2 = 4 x^2 + 6 x y + 6 x y + 9 y^2 = 2 x (3 y + 2 x) + 3 y (3 y + 2 x):
4 2 x (3 y + 2 x) + 3 y (3 y + 2 x)
Hint: | Factor common terms from 2 x (3 y + 2 x) + 3 y (3 y + 2 x).
Factor 3 y + 2 x from 2 x (3 y + 2 x) + 3 y (3 y + 2 x):
4 (3 y + 2 x) (3 y + 2 x)
Hint: | Combine products of like terms.
(3 y + 2 x) (3 y + 2 x) = (3 y + 2 x)^2:
Answer: 4 (3 y + 2 x)^2