Question

Using the formula for squaring a binomial, evaluate the following: 

(i) (69)² 

(ii) (78)² 

(iii) (197)² 

(iv) (999)²

Answer 1

(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