If $x+y=8$ and $x y=15$, what is the value of $x^{2}+6 x y+y^{2}$?
(a) 64
(b) 109
(c) 120
(d) 124
(e) 154
The correct option is (d).

Squaring both sides of the equality $x+y=8$, we obtain $x^{2}+2 x y+y^{2}=(x+y)^{2}=8^{2}=64$. Since $x y=15$, we conclude that

$$
x^{2}+6 x y+y^{2}=\left(x^{2}+2 x y+y^{2}\right)+4 x y=64+4 \times 15=124
$$