Question 2

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

Step 1 — Calculate (64)²

Let's write 64 as a sum of two numbers. We can write 64 as 60 + 4. Now we apply the identity $(a+b)^2 = a^2 + 2ab + b^2$.

$(60 + 4)^2 = (60)^2 + 2 \times 60 \times 4 + (4)^2$

$= 3600 + 480 + 16$

$\boxed{4096}$

Step 2 — Calculate (105)²

Let's write 105 as a sum of two numbers. We can write 105 as 100 + 5. Now we apply the identity $(a+b)^2 = a^2 + 2ab + b^2$.

$(100 + 5)^2 = (100)^2 + 2 \times 100 \times 5 + (5)^2$

$= 10000 + 1000 + 25$

$\boxed{11025}$

Step 3 — Calculate (205)²

Let's write 205 as a sum of two numbers. We can write 205 as 200 + 5. Now we apply the identity $(a+b)^2 = a^2 + 2ab + b^2$.

$(200 + 5)^2 = (200)^2 + 2 \times 200 \times 5 + (5)^2$

$= 40000 + 2000 + 25$

$\boxed{42025}$

Answer

(i) $(64)^2 = 4096$ (ii) $(105)^2 = 11025$ (iii) $(205)^2 = 42025$