wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Which of the following identities is not applicable to simplify
(4x+5y)2 - (5x+4y)2?


A

(a+b)2=a2+2ab+b2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

a2b2=(a+b)(ab)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

(ab)2=a22ab+b2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

a2+b2=(a+b)22ab

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

(ab)2=a22ab+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)22ab ]
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-
25x240xy16y2
=9y29x2
OR
Using Identity a2b2=(a+b)(ab),
(4x+5y)2(5x+4y)2
=[(4x+5y)(5x+4y)] ×[(4x+5y)+(5x+4y)]
=(yx)(9x+9y)
=9xy9x2+9y29xy
=9y29x2


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
(a + b)^2 Expansion and Visualisation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon