150r^2+360rg+216g^2=?

1st factor (6):
= 150r² + 360rg + 216g²
= 6(25r² + 60rg + 36g²)

2nd & 3rd factors:
25r² + 60rg = - 36g²
r² + 12/5rg = - 36/25g²
r² + 6/5rg = - 36/25g² + (6/5g)²
r² + 6/5rg = - 36/25g² + 36/25g²
(r + 6/5g)² = 0
r + 6/5g = 0

Answer: 6(5r + 6g)²

Proof:
= 6(5r + 6g)(5r + 6g)
= 6(25r² + 30rg + 30rg + 36g²)
= 6(25r² + 60rg + 36g²)
= 150r² 360rg + 216g²

150r^2 + 360rg + 216g^2
= 6(25r^2 + 60rg + 36g^2)
= 6(25r^2 + 60rg + 36g^2)
= 6(25r^2 + 30rg + 30rg + 36g^2)
= 6[(25r^2 + 30rg) + (30rg + 36g^2)]
= 6[5r(5r + 6g) + 6g(5r + 6g)]
= 6(5r + 6g)(5r + 6g)
= 6(5r + 6g)^2

6(25r^2+60rg+36g^2)=
=6(5r+6g)^2