Question

81(x+1)^2+90(x+1)(y+2)+25(y+2)^2

Answer 1

GIVEN
81(x+1)^2+90(x+1)(y+2)+25(y+2)^2
IDENTITY
(a + b) ^2 = a^2 + 2ab + b^2

Therefore, 81(x+1)^2+90(x+1)(y+2) +
25(y+2)^2
= [9 (x + 1)]^2 + 2[ {9(x + 1)} {5(y + 2}] +
[5(y + 2)]^2
= [{9 (x + 1)} + {5 (y + 2)}]^2
= [9x + 9 + 5y + 10]^2
= (9x + 5y + 19)^2

IDENTITY
(a + b + c)2  = a2 + b2 + c2 + 2ab + 2bc + 2ca

Therefore, = 81x^2 + 25y^2
+ 361 + 90xy + 190y + 342x