Question

Find the sqare of 101 without doing the actual multiplication

Answer 1

You can use the square of the binomial formula

$(a+b)^2 = a^2+2ab+b^2$

where a = 100 and b = 1 to get

$101^2 = (100+1)^2 = 100^2 + 2\cdot 100\cdot 1 + 1^2 = 10000+200+1 = 10201$