Question

(i) Find the value of $204\times 206$ using identities.
(ii) Find the value of ${992}^2$ using suitable identities.

Answer 1

(i) Here, $204\times 206=(200+4)\times (200+6)$

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

We can use the above identity to solve this question
where $x=200,a=4,b=6$

So, $204\times 206=(200+4)\times (200+6)$

$={200}^2+(4+6)\times 200+(4\times 6)$

$=40000+2000+24$

$=42024$

(ii) Here,${992}^2=(1000-8{)}^2$

It is of the form $(a-b{)}^2=a^2-2ab+b^2$

where, a = 1000 and b = 8

So, ${992}^2$

$=(1000-8{)}^2$

$={1000}^2-2\times 1000\times 8+8^2$

$=1000000-16000+64$

$=984064$