Question

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

(i) (54)² 

(ii) (82)² 

(iii) (103)² 

(iv) (704)²

Answer 1

(i) Given, 

(54)² 

If we break the given number we get; 

(50 + 4)² 

Now we can use the (a + b)² = a² + b² + 2ab 

So, 

= (50 + 4)² = (50)² + (4)² + 2 × 50 × 4 

= 2500 + 16 + 400 

= 2916

(ii) (82)² 

We can also write it as; 

(80 + 2)² 

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

We get, 

= (80 + 2)² = (80)² + (2)² + 2 × 80 × 2 

= 6400 + 4 + 320 = 6724

(iii) (103)² 

We can also write it as; 

(100 + 3)² 

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

We get, 

(100 + 3)² = (100)² + (3)² + 2 × 100 × 3 

= 10000 + 9 + 600 

= 10609

(iv) (704)² 

^{We can also write it as;} 

(700 + 4)² 

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

We get, 

= (700 + 4)² = (700)² + (4)2 + 2 × 700 × 4 

= 490000 + 16 + 5600 

= 495616