Which of the following identities is not applicable to simplify
(4x+5y)2 - (5x+4y)2?
(a−b)2=a2−2ab+b2
(4x+5y)2
= (4x)2+2×(4x)×(5y)×(5y)2
[ Using the identity
(a+b)2=a2+2ab+b2
or
a2+b2=(a+b)2−2ab ]
So, (4x+5y)2=16x2+40xy+25y2
Similarly, (5x+4y)2=25x2+40xy+16y2
Now,
(4x+5y)2−(5x+4y)2
=(16x2+40xy+25y2)-
(25x2+40xy+16y2)
=16x2+40xy+25y2-
25x2−40xy−16y2
=9y2−9x2
OR
Using Identity a2−b2=(a+b)(a−b),
(4x+5y)2−(5x+4y)2
=[(4x+5y)−(5x+4y)] ×[(4x+5y)+(5x+4y)]
=(y−x)(9x+9y)
=9xy−9x2+9y2−9xy
=9y2−9x2