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