Question 2

We will use the given identity $(a - b)^2 = a^2 - 2ab + b^2$ to find the squares.

Step 1 — Calculate $(79)^2$

Let's express 79 as a difference. We can write 79 as 80 - 1. Here, a = 80 and b = 1.

$(79)^2 = (80 - 1)^2$

$= (80)^2 - 2 \times 80 \times 1 + (1)^2$

$= 6400 - 160 + 1$

$= 6240 + 1$

$\boxed{6241}$

Step 2 — Calculate $(193)^2$

Let's express 193 as a difference. We can write 193 as 200 - 7. Here, a = 200 and b = 7.

$(193)^2 = (200 - 7)^2$

$= (200)^2 - 2 \times 200 \times 7 + (7)^2$

$= 40000 - 2800 + 49$

$= 37200 + 49$

$\boxed{37249}$

Step 3 — Calculate $(299)^2$

Let's express 299 as a difference. We can write 299 as 300 - 1. Here, a = 300 and b = 1.

$(299)^2 = (300 - 1)^2$

$= (300)^2 - 2 \times 300 \times 1 + (1)^2$

$= 90000 - 600 + 1$

$= 89400 + 1$

$\boxed{89401}$

Answer

(i) $(79)^2 = 6241$ (ii) $(193)^2 = 37249$ (iii) $(299)^2 = 89401$