1.

Using the formula for squaring a binomial, evaluate the following: (i) (69)2 (ii) (78)2 (iii) (197)2 (iv) (999)2

Answer»

(i) Given, 

(69)2 

We can also write it as; 

(70 – 1)2 

Now, 

By using the formula (a - b)2 = a2 - 2ab + b2 

We get, 

= (70 – 1)2 = (70)2 – 2 × 70 × 1 + (1)2 

= 4900 – 140 + 1 

= 4761

(ii) Given = (78)2

We can also write it as;

(80 – 2)2

Now,

By using the formula (a - b)2 = a2 - 2ab + b2

We get,

(80 – 2)2 = (80)2 – 2 × 80 × 2 + (2)2

= 6400 – 320 + 4

= 6084

(iii) (197)2

We can also write it as;

(200 – 3)2

Now,

By using the formula (a - b)2 = a2 - 2ab + b2 

We get, 

(200 – 3)2 = (200)2 – 2 × 200 × 3 + (3)2 

= 40000 – 1200 + 9 

= 38809

(iv) (999)2 

We can also write it as; 

(1000 – 1)2 

Now, 

By using the formula (a - b)2 = a2 - 2ab + b2 

We get, 

(1000 - 1)2 = (1000)2 – 2 × 1000 × 1 + (1)2 

= 1000000 – 2000 + 1 

= 998001


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