Question

Find the square of 45 by using the identity (a + b )
2 = a2 + b2
+ 2ab

Answer 1

Answer:

2025

Step-by-step explanation:

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

(40+5)2= (40)2 + (5)2 + 2×40+5

= 1600 + 25 + 400

= 2025

Answer 2

Decomposing the given number,

⇒ 999=1000−1 ---- ( 1 )

Here, a=1000 and b=1

Squaring both the sides of ( 1 ),

⇒ (999)

2

=(1000−1)

2

=(1000)

2

−2(1000)(1)+(1)

2

[ (a−b)

2

=a

2

−2ab+b

2

]

=1000000−2000+1

=998001

∴ (999)

2

=998001