Which of the following identity is not applicable to simplify (4x+5y)2−(5x+4y)2?
=
- 2ab +
(4x+5y)2=(4x)2+2×(4x)×(5y)×(5y)2
Using the identity, (a+b)2=a2+2ab+b2
(4x+5y)2=16x2+40xy+25y2
(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 the 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