Which binomial is a factor of49x^2+84xy+36y^2

(7 x + 6 y) ^2

Step-by-step explanation:

Factor the following:

49 x^2 + 84 x y + 36 y^2

The coefficient of x^2 is 49 and the coefficient of y^2 is 36. The product of 49 and 36 is 1764. The factors of 1764 which sum to 84 are 42 and 42. So 49 x^2 + 84 x y + 36 y^2 = 49 x^2 + 42 x y + 42 x y + 36 y^2 = 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

7 x (7 x + 6 y) + 6 y (7 x + 6 y)

Factor 7 x + 6 y from 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

(7 x + 6 y) (7 x + 6 y)

(7 x + 6 y) (7 x + 6 y) = (7 x + 6 y) ^2:

Answer: (7 x + 6 y) ^2