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