Question

Find value of 36x^2+49y^2-84xy , if x =2 and y=-2

Answer 1

$36 {x}^{2} + 49 {y}^{2} - 84xy \\ = 36(2) ^{2} + 49( - 2) ^{2} - 84(2)( - 2) \\ = 144 + 196 + 336 \\ = 676$

Answer 2

36x^2+49y^2-84xy=(6x)^2+(7x)^2-2(6x)(7y)
Here if we put the identity (a-b) ^2=a^2+b^2-2ab we get:
(6x-7y)^2
If, x=2 & y=-2 then,
[(6*2) -{7*(-2)}] ^2={12-(-14)}^2
=(12+14)^2
=26^2
=676