1.

Using the formula for squaring a binomial, evaluate the following: (i) (54)2 (ii) (82)2 (iii) (103)2 (iv) (704)2

Answer»

(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


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