2. Simplify the following using identities
a) (109)2 + (91)2 JS (200)2 - (100)2
(1025)2 - (975)2 (10)2 + (20)2
Answers
Answered by
3
Answer:
Answer
a)(109)
2
+(91)
2
=(100+9)
2
+(100−9)
2
By (a+b)
2
+(a
2
−b)
2
=2[a
2
+b
2
]
Therefore (100+9)
2
+(100−9)
2
=2[100
2
+9
2
]
=2[10000+81]
=2[10081]
=20162
b)(200)
2
−(100)
2
By identity a
2
−b
2
=(a+b)(a−b)
∴(200)
2
−(100)
2
=(200+100)(200−100)
=300×100
=30000
c)(1025)
2
−(975)
2
By (a+b)
2
−(a
2
−b)
2
=4ab
=(1000+25)
2
−(1000−25)
2
=4(1000)(25)
=1000×100
=100000
d)(10)
2
+(20)
2
Now a
2
+b
2
=(a+b)
2
−2ab
∴(10+20)
2
−2×10×20
⇒(30)
2
−400
⇒900−400
⇒500
Similar questions